There are quite allot of differences between the two. These are the changes that comes to mind at first:

Ranger - Goes from beeing able to use some poor white magic (original) to be able to do x4 9999 dmg at high job levels. (DS) From the back row.. the ultimate killing machine. (Can get annoying having to keep buying arrows though)
Sage - The speed is now so slow that you always act last = death
Bard - Always act first! (when you use a song) But I can't remember how it was in the original tbh.. but it's very good for tactical speed players like myself in the DS version.
Scholar -It was bad.. and it's still bad just in a different way. Now able to double dmg and double healing from items and use low lvs Black/white spells. Poor stats at level up makes it very dangerous though. And you'll probably need to combine with a thief to stock up on items.