Hi Mike, had my Hannspree a few weeks and the kids had a 360 for xmas.
I have been running the console via the component cable plus the composite connection for some early games which require the switch to be moved on the block for normal TV at 60Hz (TOP SPIN 2 TENNIS)
All I can say is I have been running the Xbox on 720p since plugging it in via the included cable. The picture and colours have been spot on. We sit about 8 feet from the TV and it looks great. Since we had Call of Duty 4 it's not been out of the machine the graphics are amazing!!!!!!!!!
I did however buy an HDMI cable yesterday and luckily my Pro model is a later one and has an HDMI port. All I can say after connecting the Xbox via this cable is wow.!!!!It adjusted the settings automatically for maximum resoultion. The game picture now is almost movie like, much sharper and the colours look at little less harsh. I did not realise it could get any better than before.
I cannot comment on using it via vga as I have no lead, but I have read many threads with concerns of tearing when playing fast moving games. I must admit like the other poster said dvds look good through the vga via my laptop dvd drive.
Often its a case of trying things for yourself and see what's best for you.
Hope this info is of help although a little long-winded, and enjoy. The Hannspree's have had abit of a bashing but I must have had a perfect one which I am more than happy with, so much so I got it for games only, but have ended up buying a freeview upscaling unit plus looking at building a media pc for it also.
Ash