Another one of the interesting aspects of Persona 3 is that every character other than the main hero is controlled by the game program rather than the player. You control every action of the hero in battle, but you can only select general tactics for your allies. While this is fairly typical, if not necessary, in action games or action-RPGs, it is a very strange thing to see in a traditional RPG like Persona 3. However, despite being unusual, I consider this to be one of the strengths of the game.
The reason I like having the allies be controlled by the game AI rather then the player is because it greatly reinforces the basic structure of the game that equates the player with the main character as much as possible. An important part of that equivalency, as well as a number of the themes of the game, is the idea that the other characters are separate from the hero and are individuals in their own right. A lot of effort was made trying to make the characters complex and believable, so that they seem more like real people than plot devices or mere team customization choices. If you don't have precise control over their actions in battle, it emphasizes their independence and individuality, which in turn highlights the fact that the hero is not independent and separate from the player. You control every choice made by the hero, but you can't control the choices made by your allies any more in battle that in day to day life. The whole effect adds to the immersive quality of the game.
Another aspect of the inability to precisely control allies is the fact that it makes the difference between the hero's flexibility and his allies' deep specialization less stifling. The other characters are controlled in a different manner, so there is no expectation for them to fight in the same manner as the hero. Instead, because the hero is the most flexible in both combat ability and control options, and the hero is needed to adjust battle tactics and scan the enemy, it simply reinforces the main hero's importance and leadership position within the team.
Another good thing about this particular system is that, unlike many games with AI-controlled allies, the battle AI in Persona 3 is pretty good. The AI isn't good enough to match what a player can do, and as such its strategies are fairly limited, but you can nonetheless expect the AI to perform quite well. You allies will heal each other when they are injured, cure negative conditions if they are given the chance, will attack their enemy's vulnerabilities and go for the "1 More" effect, will finish off enemies that are weak, and will often go for an All-Out Attack even if you have not given them the "Knock Down" command. Your allies will even learn from the enemies displayed strengths and weaknesses and pay attention to information gathered from analysis of the enemy. If an ally uses an Ice attack on the enemy and it fails, no one in the team will use any more Ice attacks against it. Other than their inability to judge opportunity cost (such as Junpei using Re Patra on an ally who stumbled when he would be better off with his own attack), the ally characters can be relied upon to act in a sensible manner, so 80-90% of the time you don't even need to give out tactics commands.
Because the presence of AI-controlled allies helps the themes of the game so much, and because the AI is good enough that they are not a burden (in fact they are capable of pulling the hero out of a tough spot), the decision to use AI control rather than player control benefited the game quite a bit.