DVI = DIGITAL Video Interface, so it should either be perfect video or none at all. Digital being either you have the signal or not. degrading video quality only really applies to analogue signals, ie. VGA connections.
i think lopri has the idea, you need a KVM switch not a splitter. i think a splitter would be more like sending one DVI output connection from one PC to multiple monitors. you are trying to take several outputs (the 360, GC and PC) to one monitor, a splitter would probably be unable to do this, as the direction of data flow is opposite your intentions. (a true DVI splitter would be more like a DVI replicator, one input, some circuits to take the single input and recreate it over several outputs. the circuits would unlikely work the other way around on digital data) a VGA splitter would work both ways, analogue signals wouldn't need to be processed and reproduced, just a simple Y cable, two inputs, one output would work the other way as two outputs and one input.
my 2 cents, hope it helps.
Cheers