Persona 3 Portable is quite possibly the best version, and best of all, you can take it wherever you go.
In terms of gameplay, the game combines role playing and elements from simulation games. You'll be playing through your chosen protagonist's day-to-day life. Each day is broken up into different segments, namely "Morning", "After School" and "Evening". You're free to do whatever you wish during these periods except during certain events such as school exams, story events, socialize or improve your personal stats. It's important to be able to manage your schedule so you spend most of your time where it counts.
Building relationships is important in Persona 3, because they create something known as Social Links. Each social link is related to the Major Arcana, not only that, but each persona is related to the Major Arcana as well. By building up social links, you gain more power in creating stronger and better persona in the particular arcana, eventually when you max out a Social Link, you'll be given the ability to fuse the ultimate persona of that arcana. Creating powerful persona with strong abilities is a must need when it comes to conquering the tower that is
Tartarus.
However, not all social links will become readily available to you; at times there will be certain events that need to be triggered or a particular item required before you can start a link. Some other social links require that you build up your three personal stats to a specific level, these stats being Academics, Charm and Courage, Academics being the main one seeing as how you'll need a strong academic level to do well during exam events. You can raise these stats using various ways, you can study in the library to improve Academics, drink a special alluring cafe to raise your Charm and even sing karaoke to raise your Courage. Once again, spending time to raise these stats take up a time slot, making time management vital.
There are differences even in Social Links when it comes to the female protagonist, mainly which a lot of the social links have now switched to your very party members very similar to Persona 4. Other changes in social links have introduced new characters as well as removed some older ones. It shows a much different story and allows many of your party member's character to flesh out more than a simple backstory found in the original. Some other story elements that have changed include particular event changes; it makes the game feel fresh once more.
The other gameplay aspect is of course the combat. The combat in Persona 3 Portable is simple turn based with a few extra things you need to know. The combat works on exploiting enemy weaknesses, in doing so, you'll gain an extra turn and knock down an enemy. Knocking down all the enemies enables you to perform an "All-Out Attack" (granted that you aren't knock down yourself). "All-Out Attacks" do massive damage to all enemies on screen and is very useful against bosses who have a high amount of HP. Figuring out the strengths and weaknesses of enemies is key, as such you can scan enemies at the start of battle allowing you to view previously scanned enemies (in case you forgot) and to scan new enemies you encounter. Exploiting weaknesses doesn't just apply to enemies, it applies to you and your party members as well, just like how you can gain an extra turn, so can enemies. Thankfully, you're able to switch Persona, granting you different strengths and weaknesses and allowing you exploit their weakness before they exploit yours. Of course, the same can't be said for your party members who are the enemy's mercy, so choosing a good party is also key.
A major change in combat is being able to control your party members directly; this wasn't found in the original. It allows a higher degree of control during your battles and makes it a lot easier since the AI isn't particularly smart when it comes to conserving energy. You are also able to defend this time, giving you the ability to ward off a knock down from a weakness once if the enemy were given the chance. As well, you can gain an extra turn from a group of enemies so long as you hit one of them with their weakness. Many of these elements are borrowed from Persona 4.
During combat, there may be an instance where you can also perform a "co-op" attack with one of your party members. In doing so will allow you to perform a critical hit on an enemy and knock it down, this is especially useful when there's a single remaining enemy, leading to an "All-Out Attack", effectively wiping out or damaging a good portion. Once the battle is over, you may be presented with a bonus; this bonus includes extra EXP, healing, items and even persona. Different cards representing these bonuses are then randomly shuffled across your screen, asking you to choose one.
Persona fusion is another element to combat. By gaining persona from the shuffle bonuses, you can fuse them together and create even stronger persona. You can only hold a particular amount of persona depending on your level, as well you can't fuse persona who have a level higher than your current. Fusing persona will also allow the fused persona to inherit skills from the material persona, not only that, but certain skills can also change at times of level up, granting your persona even more abilities. Also your fused persona will gain bonus EXP if you have levelled up your social links accordingly, so be sure to raise them.
Exploration throughout the game is very different from the original. Outside of Tartarus, you no longer control your character, rather you move a cursor around and select where you want to go, very much like a point and click. You can also bring up a menu and choose where to go directly, while it might seem like it takes the fun out of exploring the various places, it makes it much more streamlined and faster to get around, as well reveal anything that could easily be overlooked while exploring yourself. While in Tartarus, you control your character directly, and it plays very much like the PS2 version. Each level is generated randomly, and on particular levels, there will be bosses for you to battle.
New to the portable version is also being able to rescue people who are trapped in Taratarus, rescuing them nets you a reward, you're not forced to save them, but it is still something to consider should you decide to explore Tartarus. Speaking of which, there are also various sidequests which you can do, doing so can earn you special costumes and equipment, a ton of money and other items, there are also persona fusion challenges requiring you to fuse a particular persona with a particular skill. The variety of sidequests is limited, however they are rewarding and not many are in particular too difficult.
In terms of graphics, the game is very well done. It looks astonishingly close to the PS2 version, at least Tartarus does. The enemies and characters are as detailed as they were in the PS2 version and the levels of Tartarus definitely don't feel any smaller or worse on the PSP. It is however a shame that the rest of the game couldn't be the same, but probably due to size constraints, it just wasn't feasible, after all, Taratarus is a big tower. All the character interaction and scenes have been instead replaced by the use of the character portraits, this isn't really a big deal, but it doesn't feel as interactive as before.
If you enjoyed the soundtrack of the original, there are new tracks to wet your ear with in this one. Once again composed by Shoji Meguro, there are quite a few new addicting tracks. There's a new battle theme and boss battle theme as well as the after school theme, they are more or less very similar to the tracks they replaced, that strange but alluring J-pop music that you'll either love or hate, but can't quite stop listening to.
Overall, I'd say that Persona 3 Portable is quite possibly the best version of the game thus far. It has great graphics for a PSP handheld with all of Taratarus being fully explorable as well a few new additions to the soundtrack that fit the tone very nicely with its addicting J-pop sound. A lot of the story elements get changed around while playing as a female protagonist and it does a better job at fleshing out characters than before, the pacing is very well done as it perfectly blends simulation and RPG elements together without you ever getting bored of either, it always has something to keep you entertained with. The combat has been vastly improved, taking many of its elements from Persona 4. It however does lack a few things such as persona fusion spells, and many of the FES elements, one being the epilogue content The Answer. These missing elements don't detract from the game all that much and it still has a hefty amount of content for a handheld game of being nearly a 100 hours in length. While it is the third revision of a fairly recent game, it's still worth it to pick it up and play it again.