I don't have the game, but I own the soundtrack, so I hope that makes my opinions valid. :) I've also seen the musical scene videos in Japanese, and some ("Ursula's Revenge" and "The New Day is Dawning") in English. Here's my thoughts:
Swim This Way - Happy happy happy, at least in Japanese! :D It's a bit annoying, though also funny. I like how Ariel ends it with a solo.
Part of Your World - I loved this song in the movie, I'm very glad SE put it in this game. It's still a great remake of the movie version, although it's shorter than in the movie. I can't wait to hear this in the English version.
Under the Sea - For some reason, I never liked this song much in the movie. However, the KH2 version of it is great, mostly because it has both Sora and Ariel singing. ^^ I've only seen the Japanese version of the scene, but it's funny how Sora dances with Ariel, and he also says things like "Darling, it's better down where it's wetter" (or something like that).
Ursula's Revenge - This scene is great, even better than in the movie since it's in musical form. The English version was also great, and I liked Sora's comments there.
(SPOILER)"Sorry, mommy, your poopsies are toast!" Great song as well.
A New Day is Dawning - Overly happy as well, but I really like this one. ^^ It has pretty much everyone singing, including
(SPOILER)the Mermaid Princesses, King Triton, Sebastian, Flounder, Ariel, Sora, Donald and Goofy. A beautiful song in the English version, and nice lyrics too. Great work by Yoko Shimomura, this song doesn't actually get blown away by Alan Menken's songs, IMHO. An extra question, though: is the singing really as desynchronized with the music in the English version as it is in the Youtube clip? :eek:
I'll vote for "A New Day is Dawning" as my personal favorite in the game, although "Part of Your World" is probably an even more beautiful song (at least in the movie).