Although it's hardly flawless, Persona 3 has enough strengths to still make it a fantastic game.
However, some things in the story aren't explained very well. Without giving too much away, I didn't quite buy the game's explanation for certain things, and wish it would have gone into greater depth. A lot of things we are expected to just accept with little explanation. I particularly didn't like the game's explanation for the origin of Tartarus and Shadows. There is one given, but I don't know, I didn't find it very believable and thought it left quite a bit of unanswered questions. So if that bothers you, you might have some problems with this game's plot. But overall the story still manages to be very dark, entertaining, and interesting. I also love how exciting it can be, particularly during the full moon boss fights.
The gameplay of Persona 3 is divided into two parts. One is a daily life/social simulator, and the other is a JRPG dungeon crawling grind. The daily life/social simulator part revolves around how the player chooses to spend his days: going to school, then raising stats to gain the attention of his female teammates, or working on Social Links. Social Links are the player's bonds, formed with the game's characters as he helps them overcome some kind of life challenge. Choosing to spend time with a character will raise the Social Link. Social Links serve as bonuses to Persona fusion. Every Social Link has its own arcana, and fusing a Persona of the same arcana can give the Persona an exp. boost. There are 10 ranks to every Social Link, and the higher the rank, the higher the Persona will level up when fused. The Social Link system develops the game's characters, and through Persona fusion, ties into the Tartarus part of the game. It makes the game more immersible and can be very enjoyable.
However, there is something about the Social Link system that bugs me. Quite a bit. Almost all of them are with NPCs. That's right, you don't get a Social Link with ANY, and I do mean any, of the male main characters. As far as the female main cast goes, three of them require a max stat (stats will often take you at least one playthrough to max out) before a social link can be formed. There is one exception, very oddly present only in this FES version, of a female main character that doesn't require a max stat to have a Social Link with, however, it doesn't become available until the very last in-game month. This, in my opinion, is a big problem. The main cast is simply far more interesting and likable than most of the NPCs you get Social Links with. Out of all the Social Links I did, I enjoyed maybe 3, and one was the aforementioned female main character that doesn't require a max stat. This seems like such a huge waste of potential. If we where given more Social Links with the main cast, they would get far character development, and you might have ended up far more attached to them, much like in Persona 3's successor, Persona 4. Yet, the plot still sets aside some time for character development, and chances are, you'll still become deeply attached to at least one character.
The Tartarus part of the game is far more typical of JRPGs. You can choose to go there at nighttime, and it mostly serves as training ground as you prepare for the bosses that show up at the full moon. There are multiple parts of Tartarus, with a mini-boss about once every 10 floors. There are no random encounters, as you can always see the enemies outside of battle, and even get a chance to attack first and get an advantage. Battles are done in a typical JRPG turn-based combat styles. Characters fight with their Personas, and every Persona and Shadow has elemental strengths and weaknesses. Time spent in Tartarus is limited by a fatigue system: you and your party members can get fatigued and even sick if you spend to long in Tartarus, which makes them weaker in battle. If a character is fatigued and you return to the first floor, they'll leave your party for the night.
There are few problems with this section though of the game though. First of all, you can't control any party members, with the exception of the main character in battle. How big of a problem needing to rely on the game's AI varies based on difficulty. On Easy mode, it's an annoyance, on Hard it makes the game almost impossible. he AI isn't really bad or anything, but AI just can't much up to the brain of the player, and this leads to plenty of frustrating deaths. Secondly, you can't return to the first floor of Tartarus to save without losing your progress in climbing the tower, except on mini-boss floors. This means you HAVE to survive for 10 floors at a time or you will lose progress if you die. So if you happen to come across an extremely tough enemy that you just can't beat, you're screwed. If the main character dies, the game's over, so watch out for him.
As far as controls go, they work well. The game's music is mostly J-Rap and J-Pop, and the songs are pretty catchy. The graphics are good, they aren't anything special, but they're pretty enough.
Now, this version of Persona 3 includes an optional epilogue called "The Answer." I can't give to much away, but this chapter deals with the characters in the aftermath of "The Journey". You explore an area known as the Abyss of Time rather then Tartarus. This epilogue contains the same basic battle system, but no calendar or Social Link system. While the story of "The Answer" is fascinating, philosophical and psychological just like "The Journey", it tends to be a bit inconsistent with the original, game causing to have a few plot holes here and there. The gameplay, one the other hand, isn't very good. The difficulty level makes it a lot harder then the original game, which really makes the game's AI party issue frustrating as heck. The gameplay can also be repetitive, since it requires a LOT of grinding and near perfect Persona fusion, and all you really do is go through a bunch of doors and fight enemies the whole game. All in all, if you didn't like the way Persona 3 ended, or want to find out more about the story, you might want to check it out. Though, due to the bad gameplay, i'd more likely recommend just watching what happens on youtube if you want to know the story.
In conclusion, Persona 3 has flaws, there's no denying it. However, if you go into it with the right mindset, you'll be well rewarded. The game just knows how to get you hooked and immersed, and this combined with the fact you'll probably get attached to at least one character, can lead to an amazing experience few games can provide. And that, in my opinion, well makes up for its problems.