The games look better.
The fact is that very few Xbox games support the HD resolutions
of 1080i and 720p, but even at 480p--which is much more common among Xbox titles--they look better than standard-def. If you're gonna stare at something for hours, shouldn't it look good?
Garbage in, garbage out.
HDTVs look their best when fed as high-resolution a signal as possible--flip between standard Leno and high-def Leno to see what we mean. The same applies to games: your HDTV looks best when given high-resolution graphics.
Utilize that gear.
Any tech enthusiast's natural inclination is to use as much of their gear to the best of its ability as possible. Maximizing your gaming experience is a no-brainer and doesn't cost too much extra: just $20 or so for the HD connection pack.