I have both, and partly because the 6800NU is an AGP version installed on a little older machine, they seem comparable to me. The 6600GT is a great value for the money; it'll let you play Doom 3 at 1600 X 1200 at high quality pretty well with AA X AF turned off. I haven't even used those with this card, but you will likely see a big difference if you enable them (the 6800 will handle AA/AF better).
My 6800NU is the PNY Verta that was on sale from CompUSA for $200. I got lucky, apparently, as not only was it in great shape but I was able to unlock the extra pipelines and get a decent overclock out of it. YMMV! Lots of people around here will warn you off of anything from PNY.
I'd say if you're looking for an AGP card, get the 6800 if you can afford the slight extra amount of money. If you're looking for PCIe, where the 6600GT is much cheaper, get that unless you get a really good deal on a 6800 like I did.
My 3DMark05 score on my 6600GT is 3840, with a small overclock. I went with Leadtek because of the price and features, and was pleasantly surprised afterwards when AnandTech did a review of all 6600GT brands and picked Leadtek as the all-around best.