this has been beaten to death, and everybody always points out every benchmark ever done to show which one is better then which one, but here is my opinion, and it's the opinion of someone that owns both, a bfg 6800gt and an ati x800pro
When it comes to doom, it looks like the 6800 does better, when i benchmarked the two, the 6800 got 77 fps and the x800 62-66. My eyes couldn't really discern the differnce,and both were played at the same resolution with the same settings. I'm sure the 6800 edged itout, but they both play doom 3 very well.
The 6800 runs a lot warmer then the x800 during gameplay, and during idle.
Farcry, I did not benchmark them, but both play FarCry well. Well enough to turn up all the settings and enjoy it.
Battlefront, they both do well, but i have a 5600 that plays battlefront almost as well.
So who wins? I like the fact that if i leave both on all day in my office and close the window and door, when i come back, the ATI is running 20 degrees cooler at idle. 
The ATI draws less power. Thats cool.
The 6800gt has all kinds of new bells and whistles like new features to make it futureproof. Well, when a game comes out that utilizes these features, if it's next yeari'll have probably upgraded by then.
The 6800 touted it's new video processor when it came out, and from everything i read, it doesn't work.
While the x800 only touted performance gains and such, all the features they promised seem to work, so I believe when it came to the x800, i got what i paid for. I've heard the argument they cripled it by taking away 4 pipelines. Well, they sold it and on the box it says there is only 12 pipelines. It's not like they sold it to me and told me it had 16 to only find out 12 work.
I've noticed in the last month, a lot of driver updates (official) have been coming from ati, but the latest nvidia driver is july (official).
So, Ilike the x800 a little more overall. They are both good cards, but the x800pro is a god performer thats just a little more polished.
Oh, and the one thing that always gets me, half the opinions of people on the internet on which is better are based soley off of benchmarks, not always the opinions of people who actually have either card.
I've read where people say the 680gt spanks the x800.... It's good for a laugh.