The best part of Persona 4 was the characters and anime cutscens, and it’s true about many Atlus games. So it’s no wonder anime based on Persona 4 is actually very good. I think they also used same voice actors as the English translation of the game.
I’m not sure it’s watchable if you haven’t played the game. But if you did, the way it treats the original art, music and characters is brillaint.
First, as I read somewhere already, the protagonist now has a name, Yu Narukami, and a character, while it the game, he had none. And the way they fleshed out some character arcs is fantastic as well: mainly Yukiko and her story about a caged bird.
Also, let’s admit, the fights in Persona are nothing special, personas are basically a bag of spells with a shaby animation. Here, Izanagi, Yu’s persona, has some cool fight scenes.