Not only better than the first, just a downright wonderful game.
Everything has been improved, but of special mention are the combat and the camera: they have been streamlined, easier to control. That means that combat is finally fun, no longer hindered by the controls.
Like the first, the player can also expect the supreme treatment being given to the Disney worlds and characters, and the fact that the feel of each comes across as very different and distinct is in no small part due to the art department. Thankfully, the translation between 2D to 3D characters maintains the great quality one has come to expect from Square Enix and the love put in shines in every little detail.
Knowledge of previous games in the series is not required, but you might find yourself scratching your head - particularly if you haven't played GBA's Chain of Memories.
All in all, it all boils down to this: If you've played the other games and liked them, wanting to see what comes next, buy this game. If you wished the first game were more user friendly, buy this game. If you're new to the series, this is probably the best place to start, unless you can get Chain of Memories first. If you don't care much about the series, you should, at least rent it, because you will find yourself in a beautiful and endlessly enjoyable ride.