What's worth playing on Xbox 360 that's not more easily accessible through Steam or GOG? I stuck to PlayStation back then because I was mostly interested in RPGs, so I'm not really sure what's worth checking out (and yeah, I still need to play Mass Effect, even if the last game was controversial - but that's definitely better on Steam or GOG).
Forza Horizon 1 was never released on anything else (although you can play with BC on newer Xboxes), playing through Xenia is mostly fine, some occasional bugs.