I just tried a Halo 2 multiplayer game over Live on my standard (Sony WEGA) TV.
It ran flawlessly. No framerate drops or anything. The textures seem a lot cleaner, the text looks cleaner. It's very sharp, not jaggy at all. Also the menus seemed a lot faster (pressing Y for example pops up the friends list instantly when before, on xbox 1, there was a slight delay for me). The only thing that seemed weird to me was the audio. Not quite sure, but it sounded a little different (especially the voice communication quality). Maybe it was just the lag though (I was playing in Big Team Battle).
I was also having trouble adjusting to the new button placement of the Back/Start/Black/White buttons. I kept trying to press the back button to brign up the scores and I wasn't hitting anything :lol I guess I have to adjust the controls or something or keep playing until I get used to the new controller.