This is my TV:
http://www.sonystyle.ca/webapp/comme...2050&parent=TV
XBOX Halo in widescreen mode is so awesome (so is MechCommander).....heck, they're all awesome.
I'll say that Gamecube isn't as good on it (no widescreen mode, and less detailed graphics).
As for ruining the projectors in the TV, you can do it to any TV, Monitor, etc, if you leave a still image on it for extended periods of time (hence having screen savers on computers).
It is perfectly safe to play your XBOX on the big TV....just every so often (ie once ever 15-20mins) pause the game so the screen changes (or just beat the level in that much time). The only kinda stuff that would imprint on the projectors would be things like Health and Ammo stuff that is always on the same spot of the screen (but pausing changes the image, and solves this problem).
Enjoy your TV!