I can't decide on my favorites immediately, so I'll go through them one at a time and share my thoughts on each.
Sailor Moon Theme
Nice theme song! I like the lyrics (even though the "never running from a real fight" bit is a total lie). Yeah, it's a weaksauce adaptation of "Moonlight Densetsu", but I love the guitar solo.
The S.A.F. Remix and S.A.F. Club Mix go on for too long, considering the amount of vocals, is the music is just plain ruined.
Fun fact: After the first two NA albums failed to give Sailor Venus any songs, the notes in the booklet for "The Full Moon Collection" retroactively credit this song to Sailor Venus and Sailor Mini Moon.
I Wanna Be a Star
Nice, catchy song in the tradition of Lynn Minmei's "My Time to Be a Star". Totally Serena.
My Only Love
Very sweet song from Serena to Darien and a perfect addition to the scene in the episode. I prefer the original mix over the S.A.F. Remix.
Call My Name (And I'll Be There)
Nice friendship song! I think the dub might have been going for a little joke by having Raye work so hard on the song, and then it just turns out that she ripped off the "Friends" theme.
I wonder why Jennifer Cihi replaced Sandy Howell on the album version. It's hard to tell which I prefer, but I guess the album version, since it's the only complete one.
Oh Starry Night
Very sweet song. I wonder who Raye is singing about.
It's a New Day
Fun friendship / love-of-life song that ends the original story arc!
Carry On
This song, dare I say it, IMPROVES on the scene over the Japanese original! Let's face it: "Moonlight Densetsu", while very nice, is not a battle song. This song rocks!
Rainy Day Man
Very nice Lita love song.
Only a Memory Away
Ah, the infamous, inexplicable rewrite! I think I prefer the original version, but both are good. I agree with a comment that I read somewhere that said the album version is too country.
She's Got the Power
I like Stan Bush from TRansformers, and I like this song, but it's no "Ai no Senshi". It's also a bit too repetitive.
"She's got the touch! She's got the power!" Sorry...
The Power of Love
Perfection. That's all that needs to be said. This song makes you want to stand up and fight alongside Sailor Moon!
I Want Someone to Love
A very cool, upbeat Sailor Moon love song! I love this one! Wicked cool!
I Want to Hold Your Hand
Serena covers The Beatles! Okay, I'm not a Beatles fan, but this song is awesome! I once saw it listed on some dance/club album, and my mom claimed she heard it on the radio at Walmart back in the day.
Who Do You Think You Are?
Very fun Serena/Raye fight/friendship song! It gets a bit repetitive, but the lyrics are so much fun!
Daddy's Girl
Nice Lita song, even though isn't she supposed to be an orphan? Or is that just Makoto?
Nothing at All
Nice, fun, relaxing Raye friendship song. Perfect way to end the "Lunarock" album.
I'm Not Ready
A fun new Raye song recorded as a bonus for "The Full Moon Collection" album in 2002, making it the last official new NA Sailor Moon content.
Raye doesn't strike me as a party girl, though.
So I guess my absolute favorite songs are:
Call My Name (And I'll Be There)
It's a New Day
Carry On
The Power of Love
I Want Someone to Love
I Want to Hold Your Hand
Who Do You Think You Are?
Yeah, I tend to gravitate toward the fast songs.