Display resolution, off-screen or intermediate buffer resolution, and textures are going to be primary consumers of memory and these are going to vary wildly dependent on a target platform and even user settings.
A game that runs on XBOX 360 and XBox One is going to have target resolution differences obviously. Likelihood is that the 360 version is running a lower textures resolution as well. Being DX9 the lighting on the 360 version may not be as complicated as the XBOX One version which in term could have ramifications on the other render buffers that you don't see / know about.
Even on a PC some of the offscreen buffers may or may not scale with resolutions and/or AA solution, etc.
Reference back to the Killzone PS4 demo postmortem and you can see an interesting breakdown of GPU memory use for a title that is targeted specifically for 1080p use: http://www.redgamingtech.com/killzone-shadow-fall-demo-post-mortem/
A game that runs on XBOX 360 and XBox One is going to have target resolution differences obviously. Likelihood is that the 360 version is running a lower textures resolution as well. Being DX9 the lighting on the 360 version may not be as complicated as the XBOX One version which in term could have ramifications on the other render buffers that you don't see / know about.
Even on a PC some of the offscreen buffers may or may not scale with resolutions and/or AA solution, etc.
Reference back to the Killzone PS4 demo postmortem and you can see an interesting breakdown of GPU memory use for a title that is targeted specifically for 1080p use: http://www.redgamingtech.com/killzone-shadow-fall-demo-post-mortem/