I own 3 xboxes, but only 1 of mine has the hdmi output. thru my experience i have noticed a noticable difference between the component hookup to the hdmi concerning the dvd playback picture quality. also the hdmi is digital while the component is analog so that adds to the picture quality a tad,in my opinion. i personaly have noticed the best picture detail in dvds thru the vga cable. it has great sharpness of detail. but the colors do look a little washed and dont have the "pop" in the color the hdmi or even the component has. i would reccomend the hdmi output always.
How good is the XBOX 360 at upscaling DVDs? I had it hooked up via component and it went from 1080p to 480 when I inserted a DVD. I know it is because I was using component and 1080p is only possible with HDMI and vga. Is there a noticeable difference in quality from upscaling a dvd to 1080p on an XBOX 360?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic