As far as I can tell, they are identical to the US versions. I have the Japanese version of Perfect Dark Zero and the Asian version of Burnout Revenge, and they seem to be the same as the US versions (as long as you have your system set to English, the game will be in English, etc. Of course this might not be the case for games that were not originally in English -- games developed in Japan, for example, might not have English.)
I've also played online. I have had some occasional connection issues, but I think that's just due to my setup. I would think that if Asian games couldn't play on Xbox live, that they just wouldn't work at all, not work intermittently.