This game is the sequel to Persona 4 Arena and I played both of these games via Xbox 360 (I don't believe there is a difference between the Xbox and PS games though). Overall, I really did enjoy playing both Arena and Ultimax as a full story, but there were a few issues I personally found to give it only a three star.

Pros:
More Persona 3 characters!
Love the flowcharts for the story without having to worry about saving over certain data
Fighting components are mostly the same in both games, so didn't have to worry about learning new moves
Interesting references made by characters' lines during the games to refer back to P3 and P4 games

Cons:
The P3 story felt a little lacking? Maybe I was just disappointed with Mitsuru and (main) gang being withheld from fighting until later in the story because I enjoyed fighting with them
I didn't really enjoy the villain; in Arena, we got a lot of depth with Labrys, but I didn't feel like I connected with Sho Minazuki that much for Ultimax
I don't know what it was, but Adachi's voice was super weird??
This is a weird comment, but I did love the flowchart for the story, but I did like how Arena set up the story in character choices (so you browse around more freely); the flowchart is useful in keeping thing straight, but it does restrict from going too far. This is a good thing, but kind of annoying for the impatient types (like me).

Unsure:
The boss fight. Once I figured how to beat it, I found it super easy with Yu Narukami, but for some reason, I struggled as Labrys? The animation is this battle scene felt clunky (the boss was 3D while your character is 2D) and it was just a little weird.

I don't have a whole lot else to say, but honestly, both games were enjoyable and it doesn't really make sense to just play Arena without playing Ultimax (I mean, you CAN, but it sort of feels like you made a halfway effort then).