Don't know how easy it is to get VGA-out on the original Xbox, but if you combine it with a SLG3000 scanline box you may get a better looking output for an LCD/HDTV etc..
Demo vid of an X360 showing this (other vids also exist) -
[ Show youtube player ]
Lots of chat about such things in the Shmups forum - hardware section - http://shmups.system11.org/
SLG3000 - http://www.arcadeforge.de
If you do a web search for the device you'll find some more reviews, opinions etc..
P.S. Scanlines are a personal taste thing I know, but some believe it improves on the default scaled LCD image..