All the goodness of Persona 3, without the whole PS2 and TV. The PSP gets a brilliant remix of a classic RPG.
The game is based on the lives of teen age high school students (go figure...) who can fight "shadows" in the Dark Hour. The game revolves around taking classes and meeting friends and learning of their story. The tangible benefits outside of the story include increasing your Persona (basically the avatar that gives you power). This social aspect increases your fighting power which takes place at night in the Dark Hour in the dungeon of Tartarus. The combat is based on elemental principles like most RPGs where enemies are weak to one type of attack and strong to another.
That's the gist of the gameplay and what the premise is. Now assuming you read my review of the non PSP version, I am going to list the changes in this version.
1.) Graphically the game stays more or less the same. The map does not allow for your character to move around, but it is a point and click type deal for interactions in school and around the world. Going into Tartarus however, your team is entirely rendered in 3D just like in the original. Outside of those two graphical changes, the full action cutscenes are replaced with only the animation changing stills. At the loss of full roaming, you do however gain a quick access panel to allow you to warp to a location instantly rather than run through the school to get to town or anywhere from any location. The added convenience never hurts.
2.) The full voice acting is present in the main storyline, although there is none in the social links. The music has changes too, but more on that later.
3.) Combat remains outside of controlling all characters a la P4 (the game does NOT tell you that you can do that, you have to realize it on the bottom of the tactics list). This is probably one of the biggest changes to P3, but is familiar from Persona 4. Fusing personae is untouched. Social link upgrading remains essentially the same.
4.) Like in Persona 4 however there is a significant change in activities. You can work part time at places in the mall for boosts to courage and charm and academics while getting paid as well. These do not increase social links however, but are a good alternative to just studying or drinking coffee when your regular social links are unavailable.
5.) The main change to the game and why I think everyone who was a fan of the original should consider this game even if they beat it a gazillion times before is the inclusion of the option to be a female character, where the story is generally similar, but the social links are played out entirely different (You can go out with Junpei and Akihiko and others as the female and even the dynamics and relationships with female characters and other social links from the first game are different). This alone is worth the price of admission to me.
So at the cost of slight graphical toning down and some voice over losses due to data constraints, the only real drawback is that sometimes the game has loading issues with the UMD format. Even if you do data install, I've noticed boss fights sometimes take a few seconds to load (anywhere from 5 to 10), which isn't egregious, but still, not the same performance as the PS2 version.
Again this is essentially the same full blown PS2 version with no gameplay watering down whatsoever with the addition of an entirely different main character to play as and some Persona 4 gameplay enhancements. Well worth the price of admission to the show, even if you've seen the non directors cut edition.
Basically, if you're a Persona fan, get this game.