P4

AN has both a story mode and a free dance mode. The story mode is all about idols being sucked into the Midnight Show and the monsters there infecting them with some conformancy hypnotism that makes them succumb to whatever the crowd thinks the idol should be. Sexy, being an airhead, whatever. The Persona cast fights back with dancing. The themes of the game are expressing yourself and being who you are and friendship. I read the first two chapters then held down skip for the remaining eight. I'm not sure what audience the story mode is intended for but I'm not part of it at all. It was incredibly dull to get through and I just couldn't put up with it further.
The dancing is fairly simple. There are six notes--left, up, down, hoop, cross, triangle--as well as a scratch note that you trigger by hitting either analog. Supposedly there was a patch that made the LR bumpers work for the scratch notes but that never happened for me even though I know I downloaded a patch at some point. In addition to hitting the notes you can also have a hold note or unison notes where you hit two notes at once.
As you progress through the game or through free dancing, each song has a main dancer so you rotate through the cast. If you hit three scratch notes marked FEVER then one of your friends will jump in and dance with you for a bit. As you finish dances you'll get game money that you can use to buy items, costumes, and accessories. The items have an effect on the dancing by making it easier or harder (in free dance) and subsequently giving you a greater or lesser score/money reward. You want to finish the main story, buy a few key items that make it easier to maintain a combo and get more money, then work your way through the free dance.
The trophy list is actually not bad. There's one trophy that's actually difficult, which is for getting a really good score. Even hitting every note won't do it--you have to have the vast majority of those notes with perfect timing and any note less than a Great will screw you. Other than that it's just about playing through the story, playing every song at least once, and triggering a few additional Fever Dance combinations. The only thing that screws the trophy list a bit is the shopping trophies--you have to buy every item, costume, and accessory, which is a bit tedious. If you buy the items listed above you'll be most of the way there when you finish getting the other trophies, though.
Overall it's a fun game. It's not as good as IA/VT from a gameplay standpoint, but it does have dancing characters to focus on whereas IA/VT is just a bunch of notes with some fun visuals. IA/VT on the other hand has an absolutely shitty trophy list that requires playing all 60 songs at least three times just for the easy/normal/hard sets, then also replaying a number for the challenge mode and the daily challenge as well as replaying until you have 100 Perfect song ratings. Even if you're very good at rhythm games and get a lot of Perfects on the first try you're still looking at around 250 song plays.
IA/VT colorful's trophy list is super tedious and an absolutely chore to get through, but while I was playing P4

AN I was still wishing I was playing IA/VT instead. Except for when Naoto was dancing, anyway--she's the best!
https://www.youtube.com/watch?v=k6bVISe0Jic