I never had much luck running KOTOR/II on the 360, would get about an hour in and the game would break due to the poor emulation, I would not recommend playing that version. Sadly the PC versions of the game (Disc based) fail to run on Windows 7 for me, regardless of patches/compatability mode options, they crash right after the character setup screen.
I recently picked up the steam versions for cheap, haven't had a chance to test them though, hoping for the best as I really want to play with the restored content mod for KOTOR II.