All the current gen fighting games I know of that are currently out, are multiplat, other than Tekken Hybrid, which was really just an HD port of Tekken Tag, and a demo of Tekken Tag 2, as well as a silly cg movie. Otherwise, Tekken 6, and the upcoming Tekken Tag 2 are both playable on the xbox 360, though Dualshock series controllers are the only authentic way to play Tekken on a console, since it'll be the same as playing the ps1 and ps2 Tekken games, not only in terms of controller layout, but also in controller size, and dimensions. Of course, it depends how big of a Tekken fan you are. If you're a casual fan, authenticity or lack thereof won't make a difference. With other series, it really comes down to which console you prefer. I don't care for the 360's d-pad though, and I tend to use the d-pad for 2d fighting games, or fighting games like Tekken, where movement is mostly left and right.
To be honest, I'm not the best one to ask about fighting games. I'm usually more into other genres, but I'm quite fond of Tekken, and I occasionally try other fighting games. I did pre-order my copy of Persona 4 Arena, though it was backlogged till I finally beat Persona 4. It's the latest fighting game, and if you're fond of Persona 4, or the Persona series in general, I'm sure it's awesome(and it's available on both systems). Playstation Allstars Battle Royale will be coming to the ps3(and I think the Vita), so that will be another ps exclusive fighting game.