The original Summer show features the song "Natsu wo Shimashou Vacation", the revision features a version with new lyrics called "Fuyu wa Nan Tatte" (which is unrecorded) where they talk about Christmas and Snow. (Sea Sea Sea is replaced with Gin Gin Gin and Snow Snow Snow). By the sounds of it, Haruna was taking them to some mountains somwhere instead. The song "Onnanoko no Shinsou" received new lyrics too. There was also some cast changes, Yuuta Mochizuki who played Kunzite in Summer stepped up to play Mamoru and Ryuuji Kasahara took the role of Kunzite. Their outfits changed to Winter-oriented clothes, Usagi was in a sweater and so on. I only know this from pamphlets and so on, I never saw it live so I cannot say but most likely that was it for Dark Kingdom.
These are the differences I know of, other than this, we can assume the plot was the same. Early in the musical series, revisions apparently were not important or different enough to be recorded. Later revisions would have very big differences like in Sailor Moon SuperS where the entire ending changed or Transylvania no Mori where its main villains were swapped in terms of importance. Sailor Moon Musical information in the English fandom is often misunderstood or confused, even ones purely dedicated to myu, the best way to understand it is to watch it yourself. I have read things like "Professor Tomoe is played by Kazuko Ono" (Kazuko Ono is a woman playing Lamia...) "Loof Merrow, a space pirate..."(Loof Merrow comes from Earth...) and so on...