This is probably an unpopular choice and I imagine I'll get chased from the internet by users, pitch fork and torches in hand for saying this but I'm going to go with UFC: Undisputed 2010 for the 360. I would have went with Fight Night Round 3 because that game was a blast to have around, specially with friends but sadly I think FNR3 came out way over three years ago.
So I'm going to go with UFC: Undisputed 2010, I thought it was a great improvement over the original to the point that it made the 2009 game almost unplayable. The game had a great degree of customization, maybe not in the appearance side (well the clothing was varied but it was limited in the whole fighter creator department) but in the move set, you could pretty much create your own fighting style here which was awesome. I liked how it was announce your first and second name along with your nickname, it was a nice touch, sadly it didn't have my last name but it did have a few friends names and it sounded awesome.
I thought the combat was awesome, the story mode was good though not faultless, it had a good roster and a pretty good game if your part of the fanbase.
I had more fun with it than I did with most fighting games I played in the last three years. Which is probably going to get me burned at the stake for saying but thats my opinion on the matter I hope you guys and gals respect it.