I bought this for my Xbox 360, after checking to see if it would work. Online research led me to believe it was compatible, but to expect loss of music and occasional crashes which could be overcome by reloading from a saved game position. Since I usually turn the music off when playing games I was willing to put up with the occasional problem for the promise of exceptional gameplay.
The reality is that it loads, very slowly, and can be played, just, with excruciatingly long delays (several minutes) whenever you attempt to look at an object, open a door, interact with anything etc. I got part way through the introduction over a couple of hours last night before giving up in exasperation. I only stuck with it for that long because I was able to get a taste of the atmospheric, immersive nature of the game, and really liked it.
My solution to the problem will be to buy an old Xbox from someone on ebay/Gumtree for £25 so I can play it properly.
My apologies for posting a 3* review for a game I have yet to play properly, but I hope this information will be useful to someone else who might follow the same line of research and be tempted to buy it for his Xbox 360.