It's probably a toss-up. Right now I happen to like nvidia and although my first 6800GT died, I've been happy with it's replacement. The drivers are pretty stable and if I recall correctly, AH runs just a bit faster on nvidia hardware than on ATI. But that's a recollection from over a year ago, after HT had made some major changes. I don't know if HTC has been able to get any speedups on the ATI cards lately.
There used to be framerate test threads in one of the forums while HTC was beta testing some graphics optimizations, and that may give you some clues as to relative performance, however the framerate tests can't be directly compared computer to computer because the test didn't lock down the graphics settings or screen resolution.
If you play quake or doom, then nvidia may be a better bet. For the desktop, I think they're about the same. Some cards have VIVO features, and some are capable of HD output via s-video or AVI. You'll have to check the individual card specs to see what features they've included.
The feature I really want is only available in the brand new ATI 1800 series cards though, so I'm going to keep my 6800GT and sit tight for another generation or two. Ever notice that with most cards today, a boulder will have one or two "sharp" looking facets and the rest of the boulder will be totally blurry? Or at certain angles, even up close textures will blur out? Well, ATI has a mode that pretty much eliminates ALL texture bluriness at all angles, out to the max visibility range. Yea it has a framerate hit, but at least it's a driver option NOW. Nvidia doesn't even try, and that means that my pet peeve of visible texture filtering thresholds (seen as horizontal lines where it's blurry on the far side of the line) isn't even on the drawing board for Nvidia while ATI has given a pretty good hack at it.
The Nvidia 7800 has better antialiasing I think.
But you were talking about the 6800GT vs. x800XL, and I'm not really sure. 3Dmark2001SE relative benchmark performance USED to match up pretty well with expected AH performance, but I haven't done any checking after HT's latest round of optimizations so I don't think that holds true anymore.