It's an actual sequel to arena. Quite a few people think of the Arena game as "just a fighting game with persona characters" but it actually continues the story from Persona 3 and 4. If you only play the new persona 4 arena ultimax, you will be missing out on some things in the story mode that happened in arena.
I really love Persona series but never tried Persona Ultimate... because I just personally hate those fighting games. I never knew there's a story behind the game! I gotta try it