Well, style mostly. Lots and lots of style.
Beyond that I don't think it really does much "so right". Not that it does them wrong, but I wouldn't say it does them any better than other JRPGs I've played. But take this as the opinion of someone who has never played a Persona game prior.
The biggest criticism I have is the whole time management, which is on auto-pilot more than half the time, giving you at best two time slots a day. And that's only if the game doesn't decide you're not allowed even that cuz reasons.
The level design of the Palaces are a bit samey and not even that good to begin with. You're just running through corridors every time.
The characters, while likeable, become pretty one-note once their moment of triumph has past. Ruiji started out as my favourite character, but now he's just the dummy always saying dumb things cuz look, he's such a dummy. Same for Yusuke and Makoto.
The turn-based combat is great, except on the few occasions where it suddenly throws an insta-kill move at you. But overall it really allows you to string some cool shit together.
And after the first Palace the story becomes extremely predictable. It more or less falls into the same notes from then on with every new target. The only one that changed things up a bit was Futaba, but after that it was right back to the formula. I haven't finished it yet and I do feel like some twist is about to occur, but that doesn't change the fact that every target/Palace apart from one was the same just with new wallpaper.
I do really like the game, but I like it inspite of a lot of its awkward mechanics and level design.