The 360 auto-optimizes whatever connection you use to the best resolution it can. I'm wondering also when I open mine finally during Xmas if I can hook it up to not only our 42" HDTV LCD, but also my 21" LCD widescreen PC monitor I have. Be sweet to hook it up in my room too on my PC monitor, then again, my monitor has HD built-in already so it should look crystal clear I hope.
I figure even with regular settings on an LCD, the resolution and stuff of the monitor would be better than a standard TV anyways, so it should still look pretty darn good regardless. I mean ****, regular xbox looks awesome o standard TV to me still. I'm sure when I start using my 360 though I won't be advocating that same quote at all however lol.