Here's how it seems to me:
Fighter: Still the same butt-kicking guy with swords.
Thief: Stronger, both in attack and health.
Red Mage: Less useful, due to th implemention of MP.
Monk (BlackBelt): Same, which isn't that good in my book.
Black Mage: Better, due to the implemention of MP.
White Mage: Better, due to the implemention of MP.

The reasion the BM and WM are better with MP is because now you can cast NUKE/Flare and FADE/Holy EVERY TURN if you want, which is useful against Chao and the extra bosses. But this is from my experience.