Sorry to drag this up, but please stop posting about this kind of thing, because I can guarantee you've clearly NEVER touched on any 3d work or real-time rendering.
Sure, the XBOX may be capable of playing games at 1080p, but as of now there are no AAA games than do it on the 360. Forza 720p, Halo 3 640p, Halo:Reach was the first Halo game on the 360 to manage even 720p, after nearly 10 years. COD (all of them) are 600p, Alan Wake 540p, FFXIII 540p.
The ONLY games the 360 has a hope in hell of playing in 1080p are low-fidelity, low-detail 2d/2.5d shooters and platformers. Nothing on the 360 with even medium-quality lighting or detail will be able to go 1080p. There's JUST NOT ENOUGH GRUNT.
The PS3 is similar, except that it's first-party (and only first-party) games have been doing 720p and 1080p (Wipeout, for example), from day 1.
Yes, disc capacity does have an effect on game resolution. I don't care if you can run Doom at 600p or higher, because it's going to look worse than your grandad's old slides projected onto a movie theatre. Deal with it.
Higher resolution implies higher detailed textures, higher detailed models, better animations, and this is where the 360 falls flat on it's face. This is why Reach only just managed to pull Halo into Digital (720p).