The story is just good fan service in general with having P3 and P4 casts be in the same game. The overall story is fine and continues where both P3 and P4 left off. It's required info if you deeply care about either persona game. It's not as good as the RPG games are but it's a neat story mode that is done well enough.
I haven't played a BlazBlue game yet I found P4A to be a challenging game to be great at but it isn't too difficult to be decent at it. The multiplayer is probably dead by now so the main reason to get this game is for the story.
P3 is required if you want to get the most out of P4A.