Nobuo Uematsu is THE MAN, THE GOD, THE LEGEND that wrote all Final Fantasy music up until FF9 (to this point he was responsible for writing EVERY single piece of music in these 9 games). He did -some- music on FF10 (mainly the theme, To Zanarkand which Ora has already mentioned), he created the original soundtrack to FF11, and the CoP End Cutscene Song (the only one with Lyrics). The theme for FF12 and the Concert songs for FF10-2. All game music after FF9 is made by various other people other than the ones stated above.
Utada Hikaru has 2 songs on Kingdon Hearts 2, though they were not made specifically
for KH2, and they are the Theme and some other cutscene music (that was rearranged into an orchestral version for the game).
HOWEVER, I had a rifle through my FF Sheet music collection (I got the FF9, FF10 and FF11 all on Scoresheet in bound books :>) and I believe the song that is closest to what you are after is...
Suteki Da Ne. The sound on this video isn't the best, but it is the best performance you'll find of this game outside of the guys who actually did it. MMLeung is a musical genius of the Game Music kind.
If this is it, wooo. If it isn't, sorry. :< But other than more to follow on, I can't pinpoint what you are after. Also, I'm not that up on KH Music.