@magicalclick: It's probably best to think of the XboxOne as two completely independent machines, one running the xbox dashboard and the other a dedicated environment for the currently running game. On top of that is some magic to glue it all together. The important thing is that a Hyper-V like system fully isolates the resources even though it's the same physical hardware, ensuring that one half never effects the other.
So there is a chance that in split screen a game might run a little bit faster as the compositor has signalled to the game that it's only rending to 960x1080 rather 1920x1080, but the speed of the games render will not be effected even if the app side is maxing out it's share of the GPU/CPU resources.
This is all speculation based on rumour of course, guess we'll know for sure on the 22nd.