The first game's got a bit more of a serious tone. The graphics are nicer (obviously), and the missions are set up a bit differently.
Instead of having the map of the school, where you pick the different destinations, the first game is set up as one large book. Each dialogue scene/mission is a little section from this larger book.
There are a lot less missions in the first game, but they're a lot longer, and take place on individual large maps, instead of multiple smaller ones.
Gameplay's pretty much the same between both games though.
I'd say both games are pretty equal in all regards.
The only thing that would come down to a matter of preference is the tone of the games.
From what I've played, the second game has more lighthearted moments, taking place in the school, while the first game is a bit more serious. Things are starting to get a bit crazy though, so I can't really say for sure.
I unlocked a couple new character classes in the second game, and just realized that each sub job class further splits into another two job classes. Lots of choices.
Also: If your character gets shot down, then touched by the opposing team/sits there 3 turns without getting rescued, they get hospitalized for 3 missions in the new game. In the old game, they're dead for good if this happens.