There are many ways to do sequels in the video game world, but the most common can be summed up as "More of the same, only better." Keep what was good about the original game, tweak the things that can be improved upon, and fix anything that was broken. By that logic, Final Fantasy Tactics Advance 2 is a resounding success.
The primary problem with the original Final Fantasy Tactics Advance was a lack of easily accessible information. The GBA's screen was just too small and low-res to contain the large amounts of information a relatively complex RPG really needs, and the move to the DS fixes the problem as expected. It also adds more quests, more classes, more races, and a few other innovations that generally work to the game's benefit.
The worst of the new innovations are a set of quests called Clan Trials, which offer significant benefits, but can be excruciatingly repetitive. Also, the twenty new classes and two new races are somewhat weak, as many of the classes are redundant or even outright bad, although there are a few gems like Raptors and Tricksters.
Final Fantasy Tactics A2 also has some fun with traditional RPG tropes. The characters at one point talk about how, death is rare in the game world thanks to healing magic and resurrection items, winking and nodding at decades of RPG fans who've made the same point. Even better than that, FFTA2 fixes the age-old RPG problem of new-town/better-items by adapting Final Fantasy XII's "Bazaar" system, where defeating enemies gives the player random items which can be traded in to unlock new items. The plot, meanwhile, is trifling, and the game realizes this and happily spends virtually no time on it, recognizing that the player wants more questing, less talking.
Square Enix has their tactical RPG form honed to a science, and it shows with Final Fantasy Tactics Advance 2. Veterans of the form will find significant improvements and interesting new quests, while newcomers to the genre will discover a game that's fast and easy to play, but filled with action and complexity. Highly recommended.