Crystal Tokyo would be completely leveled, and atop its ruins would be built Black Crystal Tokyo, using the Black Crystal. As there's already monoliths of it shot into the city and it would be paying tribute to the power which allowed the Black Moon Clan to do this in the first place.

Given much of the city's former inhabitants were wiped out by the first wave of attacks alone, Black Crystal Tokyo's populace would more than likely consist of Black Moon Droids (which by the way they had no problem using to replace the inhabitants of 20th Century Tokyo). The rest of the world outside the city, in accordance to the Clan's ideals, would be restored to how it was prior to the second Silver Millenium. Meaning it would no longer be unified under a world-spanning monarchy and there would be no more unnaturally long lifespans. Lastly, the White Moon would be destroyed and Nemesis would take its place above the Earth's orbit.

This of course is how things would only be initially. The organization's ideals are bound to corrupt over time and infighting sure to arise. For instance, Demande will want to extend his control beyond just the capital city and to rule the world with an iron fist in hopes to fill the void in him brought about by Neo-Queen Serenity's death, which would in turn conflict with his idealistic brother's worldview. Things would fall apart relatively quickly and descend into chaos, which is fitting considering the Clan was being manipulated by an incarnation of Chaos.

  If Usagi and the others failed, it would take the form of one to two alternatives.
1. If they failed before killing Beryl, Beryl would've taken over and kept Mamoru as hers forever.  However, eventually, she would've turned her back on Queen Metallia because in both the Manga and in PGSM, Beryl understood how power-hungry and dangerous  Metallia was and to take extra precautions to try and find a way to defeat her on her own terms.  In both versions, Beryl probably would've became an actual anti-hero/anti-villain type of character because in essence, she's not actually that evil. She's just twisted in hatred and jealousy.  Once both those things are quelled with her possession of Endymion/Mamoru, she'd probably fight back.  Considering she had/has control over the Shitennou, she could be successful.  Then, also, having Mamoru and thus *would* eventually 'marry' him would make her the lawful queen of the Earth.

2.  90s Anime Beryl/other possibility, would've taken over but would've remained a puppet to Metallia. The earth would've been throw in a chaotic state of almost never ending fights because Metallia thrives off the negative/excess energy generated by humans. As long as humans hate/exist/ect, she'd have a never ending supply. If, for whatever reason, they get in contact with the worlds outside of the Solar System, they may begin trying to invade others to expand Metallia's control.

This is a two-parter.

90s Anime version with the 'Doom Tree' arc. If Usagi and her friends failed to stop En and Al.
1. Both Mamoru and Usagi would've become captives of the two until either En or Al, driven by jealousy, kills one of them. The entire earth would become food for the Tree and it would've taken over, influencing others and draining the life energy out of the world until the last drop before leaving Earth as a dead rock to continue it's parasitic ways as it will never have enough energy to talk to the two aliens and tell them what its' true wish was. 

*Black Moon Arc*
This one is tricky because time travel will make it harder, not easier to understand. Plus, the BMClan could accidentally wipe themselves out if they weren't careful. (which..they barely were).

90s Anime- if Usagi and them had failed. 
The Origin of the BMC is completely different here as they're descendants are from out side of the Solar System. Therefore, they're more like invaders than not. (Outers, ya'll are slacking here guys.)
There's Two or so possibilities here and they all depend on when they get to Chibiusa <- the main reason they do anything.

1. If they captured Chibiusa early enough, they would be able to weaken the future barriers and thus take down Crystal Palace and completely take over because they have the crown princess under their control.  At this point, it's only a matter of if they can puppet Chibiusa for their own means.

2.  If Diamond became aware of Sailor Moon earlier, he would've order her capture while also getting Chibiusa as well. Since he's essentially kidnapped the future Queen (who'll no longer be queen at this point), he would force her to do whatever she wants. Usagi would become a shell of her former self, miserable, and alone because her friends would most likely be dead at this point.  Which means, the future changes/future Inners are also all dead. 
 This may include Mamoru- maybe. He has a weird way of surviving things, so King Endymion might be around but he probably would've awoken to the revelation of Helios and Elysian much earlier and there probably would've been a rebel fraction.  The people of earth would be splintered in trying to decide whether they should side with the BMC or go on it alone.  There would be wars/battles for generations.  And since this is the 90s anime and we're not certain or given any assurances that longevity is a thing that the Silver Crystal can do- nothing much would've changed about the population's lifespans and would not be a factor.

3. Getting Chibiusa early at any point and time after Usagi and them fail to save her. (this is also enfolded with the idea that they failed to persuade her to rejoin the good side.)  She would've become Black Lady and eventually probably gotten on with Diamond but not for love. It's more like to prove she could be a grown up lady and this is what Adults do.  Also, Wiseman would've controlled every aspect of this union and their government the moment the legitimate heir, Black Lady, takes possesion of the throne since everyone else she knows would've died at this point- except for Moon and Tuxedo, since they *have* to be together in order for her to exist.   Diamond would be pacified by having the crystal coffin that contains NQSerenity as a trophy, but never told of Sailor Moon or Tuxedo Mask being alive.
The world, at large, would be under-siege by Black Lady's new court an armies that enforces her rule on them all with Wiseman at her side.
Sapphire would still be mooning over Emerald, who's still in love with Diamond, would've been angry at this too, because this was NOT the plan and how could his brother do this/allow this.  He may, since this is his 90s self, leave the BMC all together to fight against his brother in the long game, taking the Akayashi sisters with him. At some point, he'll find a way to travel back in time on his own to find Sailor Moon and Tuxedo Mask to help him.  Now whether they will or not, is questionable as they're still reeling from the loss of the Inners.

Manga/SMC Version:

Again, it depends highly at which point does Sailor Moon and her group lose.

1. If they lost at the Grand Finale, all of earth would be gone because the Death Phantom would've destroyed earth in order to consume the Silver Crystal.

2. All of time and space would've imploded because Diamond put the Silver Crystals Together and Pluto did not arrive to stop it. 

3.  If they failed to turn Black Lady back into Chibiusa, Black Lady would've taken over, killed Diamond, and ruled the world as she believes she should with Wiseman at her side. She would've turned the world into a true dystopia because she'll be taking out her past hurts and childish thoughts on the world itself because it rejected her (so she believes.).  It's a toss up on whether she'd kill her parents or if she'd leave them to be in the ruins of the old palace.  I have a feeling that she would've tried to have destroyed the palace out of a tantrum, really. To show that she's 'more grown up' and 'powerful' than they ever were and she didn't need them.

4.  If Diamond had succeeded in taking Sailor Moon and the Inners never being able to get her back- the future would've changed completely. There would be no Crystal Tokyo, there would be no Chibiusa, no Wiseman, or even the Black Moon Clan. Earth would be completely as it was with minor differences and more conflict.  There would be no long life, there would be nothing.  Diamond and his group would exist but they wouldn't have any powers that were given to them by Wiseman.   There would be areas that they wouldn't be able to go to because Wiseman's past self had taken over that area due to his psychic powers.  

Super-
90s Anime version

The wolrd would become a dead planet because of Master Pharaoh 90's coming and drained of their heart crystals.  Chibiusa would've died for good. The world would be overrun by monsters. Tomoe would be the mad scientist standing next to Mistress 9 and devote follower. 

2. If Sailor Moon and them failed, the only course left for them would be to abandon earth completely for a time being and retreat to the moon where they could rebulid the moon Kingdom again. There would be no contact with Earth during this time and Earth would fall into a weird hybrid sort of world.

Bonus: If the Outers had their way, none of this would've happened or a chance to happen.

Manga/SMC:

1. The world would become a graveyard because most people's souls or 'hoste' would've been taken. There would be very few humans left as the merging between Alien and Human would've happened here thanks to Pharaoh 90s and Mistress 9's union.  There would be very few sucessful unions of Alien implanted in Human bodies.  Even fewer would be those that could co-exist as most aliens would've devoured their host's hoste/souls at this point.  Chibiusa would've died and remained dead.  Mamoru would fall ill because of the adverse effects it has on the Earth, which he's connected to.  He may actually discover Elysian in this arc first and use it as a refuge for the last of humanity and the Sailor Soldiers that are left to help.  Sailor Moon may or may not be dead in this scenario as well, since she could possibly be in a magically induced coma within the Mistress 9-Pharaoh 90 hybrid. 

2. Earth's Military would try to take on the mass that is Pharaoh 90 but may only be able to make Japan a 'No Visit/Livable' zone forcing the inhabitants to either hide out in places there or move to other nations as refugees. While the interior of the country runs wild and ends up more or less overrun with human-alien hybrids that might take human form or monster form.

Again, split difference here.

90s Anime if the heroes failed-
Nehellenia would've taken over Earth with the power of the Golden crystal. Now, while she has her beauty, she may be able to concentrate on other things and see what's actually there. There's two ways to go with it. 
- 1. She might actually end up becoming good through this because she might actually recongize that the praise for her beauty is meaningless and she actually wants companionship. She'd probably eventually speak to Helios, since she has him captured, and through their talks, things could progress differently.
-2.  She becomes increasingly paranoid and plunges earth into darkness and nightmares where daylight is nothing more than a dream itself. The people of earth would've adapted to this but be a tad more miresable than usual.


Manga verse- Depending when it happens.
1. If Queen Nehellenia succeeded in getting Q. Serenity to her side, she would've taken over the moon completely and kept Q. Serenity in some way. She would've corrupted all the little inner soldiers.  There could be a possibility that P. Serenity may have been smuggled out to the outer realms to grow up. (Neither Artemis, Luna, nor the Crows are seen in this part and it's assumed they came later on.)
2.  Q. Nehellenia would've sealed the queen and princess away in darkness and then eventually gone to earth after the golden crystal.  She may end up taking the prince or whoever the crystal holder was at that time as her own.

3. Mamoru and Usagi would've died of the curse placed on them, making Nehellenia's control complete and the other Soldiers unable to truly battle against Nehellenia and her nightmares. Chibiusa would've vanished.

4. If Nehellenia succeeded in getting Mamoru, she would've sealed all the sailor soldiers away. Chibiusa may or may not disappear and the future would be entirely different.

90s/Manga-
Galaxia would've won and just destroyed the Earth.  That's it.  That's what she does in both versions that exist.  She comes in, takes what she wants, deems the planet not fit for her, and destroys it.

90s-
Chaos would've killed P. Serenity, taken over Earth, and moved on to more Sailor Crystal-gathering, giving Galaxia control of her body again and continue the rampage across the galaxies.

Manga wise-
Chaos would continue on to obtain more stars/Sailor Crystals in order to become a true Star itself. With Sailor Moon's Sacrifice having failed, it would've converted her Sailor Crystal into a Chaos one and take on her sailor crystal itself as it has shown to be super powerful which may be enough for Sailor Chaos to come into being. 
This would ALSO possibly be the reason why Sailor Cosmos exists as her purpose was to fight against Sailor Chaos. Their battles probably ended many galaxies, leaving Earth and it's Solar System as one of the last ones left to do battle on, which in turn could be the place Sailor Cosmos ran away from to try and start things over again, thus creating a time loop of their never ending battle.  (Basically, Timey-whimey things happened and this AU could be the reason for Cosmos and Chaos's existence in the first place in another timeline but because both can travel freely through time and dimension, it's easy to see them cross other time periods like this. )

Since Queen Metalia seemed interested in the destruction of the Moon Kingdom, the world would probably be destroyed. If Beryl and the Shitennou plus the Earth were allowed to continue existing they'd probably reestablish the Earth Kingdom. Although they probably wouldn't have the Silver Crystal to confer the kind of utopia Neo-Queen Serenity would formulate, I somewhat think that they would rule fairly decently, as they did during the Silver Millenium, though they might decide to exterminate all the existing living things first. Also, when Galaxia comes around they'd probably resist and get destroyed.

Wiseman also doesn't really seem to have much really planned except destroying Earth, and maybe ruling over some kingdom on Nemesis. The Black Moon would probably do the same as the Dark Kingdom if they were allowed to continue existing, and set up their Black Moon Kingdom. Considering their outlooks though, they might descend into fighting again, each other or maybe Galaxia when she arrives later.

Pretty much Pharaoh 90 and the Tau Star System replace the world and probably cause severe gravitational effects from doing so, unless magical stuff resolves that sort of issue.

The Dead Moon victory would probably be like the Dark Kingdom's victory, except with more CIRCUS, and probably also would eventually be destroyed by Galaxia.

This one I think would be quite interesting, and would be really fascinating to think about. Would Chaos be satisfied when the Silver Crystal is destroyed or united with it, if the antagonists of some of the previous arcs were successful? Would Sailor Galaxia, Sailor Cosmos, or Chaos, upon taking control of the Cauldron, come to a similar conclusion that Sailor Moon did?