Dissidia is a great fighting game, and has tons of unlockables.
Controls. Easy enough to use. But even if you find them to be too much, you can go classic with a command style control scheme. So they can develop to your style.
Levels are nice. One from each final fantasy , except 11 and 12. They are from the Chaos's characters lair, or final battle(or around that..Ex - Ultimicia's Castle - FF8)
Story - Not much, but it's a fighting game, so what do you expect. End of the world, the warriors of Cosmos need to save it.
Extras - Tons. Enough to keep you entertained for a long time.
Different modes to unlock to provide more challenges.
As for the fighting, Square-enix did a great job, but can get a bit cheap when fighting higher levels. They can break your bravery in one hit, followed by a one hit kill. They also tend to use the same attack over and over and over, until they kill you.( EX: Story Mode- Onion Knight vs Terra - Terra has pretty much unlimited Ex [like limit break] and repeats the same move, which has a big range, as soon as the last one is finished, making it almost impossible to counter. But that is probably the only problem.
Anyways, one of the best psp games to date, and if you want a fun game, fighting game, or FF game, i recommend you pick it up.