For me this is a tie:
1) Alpha Protocol - First of all I love this game. Secondly it's complete shit. The best way I can describe it is it's like Mcdonald's Hamburgers. It's delicious and filling upon consumption but 15 minutes later all you feel is regret and despair. I think the attraction here is unfulfilled potential. If given the "Mass Effect" treatment in the polish department this could have been my favorite game on 360. As it sits right now it's a buggy mess with a compelling story that brings me back every few years.
2) Fallout New Vegas - Many of you know of my trials and tribulations with this particular title. From game breaking glitches to corrupted saves I should on all accounts hate this game. Unfortunately I'm a die hard Fallout fan and NV (when it's working) is a truly great game. I just wish the glitches were fewer and less frequent during my time with it.
Honorable mentions: Resident Evil 6, The Last Remnant, Kane and Lynch