Disclaimer: I played P4 before watching the anime so my views might be skewered to those who played the game without taking much consideration to the numbnuts (Most likely you, unfortunate, miserable reader) who haven't played the game. I'll try to bring myself down to your slime level and... offer views on the uninitiated. Or what I think it would be like if I was as pitiful as one who hasn't played it.
After this is said, highly unlikely I'll follow through.
Story: Straight up, play the game. The game is better than the anime and the game is sublime, one of the greatest things to be released on Earth. The anime, it's pretty dang darn good and does it justice but to get the most you can out of it, invest 80 hours into P4 (Really, it's a long ass game).
Ok, it's a murder/mystery at heart with elements of fighting, school life/slice-of-life and character development. More on the non-genre one later. The murder mystery itself is pretty good, but I think you'd be there more for the ride instead of playing Sherlock. You may be given clues and such, but chances are you're not keeping track since you mostly know what they (The investigation group) know. It's real cool and all but the real meat lies in the events outside the mystery; the social aspects and events.
Events first and if you've played the game, they're just as good. Barring a hilarious line in the culture festival (You know the one), they pretty much play out just like they do in the game. They usually have the same stuff that make up the event and a few are even added on to it's benefit. Some are hardly plot-relevant and are there for kicks but others help dig deeper into the plot, if not move it forward in some way. The events are those you'd see in a regular Japanese school year and are a real treat. Most are comedic and a few are even laugh out loud funny.
While some aid the plot, others aid in character development. By going more into a character (And possibly his/her motives), we're expanding the story AND providing fun! Two pies for your buck! This (Sort of) is where I'll mention the social aspect, and by that I mean "Social links", which is a fancy term that basically means character development. The game has 16 or so links and the anime has 26-ish episodes, so obviously not all links can be as fully fleshed out as one would desire. I was kinda miffed that they weren't but it would be hard to fit 'em all in and keep the viewer's attention, with them believing it's filler of sorts. The development is uneven, some are given more attention than others and one is even excluded (Kinda like the game). What's there is there, and it's done well enough.
There's also the combat, which plays a hefty role in the taco of things. It's where the Persona component comes into play and where some of the development and action lies. Done pretty well too, glossing over most of the fusions (Narukami would be fusing all on his lonesome in the Velvet Room) and fusions at improper times (Level-wise) is nitpicky. The fighting is fast, it's engaging and it's actually pretty damn faithful to the game.
Among all the comedic moments are the sad, emotional segments. There are a few that can be real tearjerkers and others that come through character development. Has some real heartfelt moments and are not just tacked on.
Animation: Thanks to greektornado, I notice the spaghetti sauce on their chins. So noticable when one notices it. Demerits but points for how good everything looks otherwise and familiarity. It's fanservice for the veteran, as the characters look good, the personas look gnarly, things are rad and Naoto. Naoto full stop.
I'm uh... forgetting... for... ah screw it. Animations spiffy.
Sound: Oh god yes. It's a total eargasm. There's an orgy in your ears and every note is invited. The music, oh lordy lord... I remembered the tunes, it has Heaven, The Almighty in the most perfect place (And missing in another), Reach Out to the Truth and the school trip, fans would be clapping their hands in glee. This is as good as it gets, and as faithful as can be with some bloody hilarious placements of Muscle Blues. No OP from the game, but a minor quibble, as good as it was.
No problems with the VO, except for Teddie in one part. No preference for dub or sub but if I had to choose one, dub. Maybe. Narukami's actor in the dub hams it up and that's always a plus. And for the sub, onii-chan.
Characters: Liked them before, like 'em now. The main group gets developed, a few of the people outside the group get their own development, some more than the others (Social links again) and everything is fine and dandy. The group has chemistry, each person has their own demons and they're more than just a name. Although some characters are more... trait-excessive? Like a character's trait might be more prominent than it should have been.
Aside from less development in half the social links, I don't have much to say. I have my favorites, I have those that I just adore and those I wanted to see more of. But should mention the delivery gal for the noodle shop, her deadpan delivery and deliver anywhere motif is hilarious.
Overall: Spent more time on frivilous (Needless) details but end point, I loved it. I got the callbacks, the references, felt the nostalgia after playing the game a few months prior (Gross misuse of nostalgia) and the music, crowning moment of everything.
A person just entering the series wouldn't have as much enjoyment and should be directed to the game, if possible. If not, feel free to give it a go. It takes a few episodes to pick up but it's still a fun watch, has it's comedy and drama, development and an OVA that warrants a watch. Entire thing is mandatory for those who played the game and can more easily pick it apart.
The music, oh lordy lord... I could give this a 9.5 overall based on that alone.