Dissidia: Final Fantasy is an action RPG on a portable system that's jam-packed with the kind of features you would expect in a Final Fantasy game on a non-portable system.
The heart of the game is a fighting game set in expansive, full 3D environments. The combat system itself is more in depth than your typical button masher and is somewhat overwhelming at first. The game also lets you take full advantage of the 3D environments by, among other things, running up walls, sliding around on rails, and fighting in the air a la the final battle between Cloud and Sephiroth in Advent Children (though you can't actually fly).
There is a story mode where you play the main characters from FF I - X on their quests to save the world from the ultimate evil, blah blah blah. There are also a number of other non-Story related Battle modes that let you fight against a CPU-opponent or another person in ad hoc mode.