I guess I'm swinging back towards ATI again, just to be on the safe side. I can always pick up an ATI silencer if the thing is too loud for me.
Anyways, the general verdict from other threads I've seen is this: At stock speeds, they're about the same (allowing for ATI and nVidia's inherent strengths and weaknesses), with the 7600GT maybe having a slight edge.
The 7600GT runs cooler and quieter. It also has Shader Model 3, but it is the opinion of many that this is not a large consideration at this price level, since by the time games come out that make more than cursory use of it, these cards probably won't be great performers anyway. Still the 7600GT has the feature advantage here. Finally, all of the 7600GTs I've seen have dual-DVI, which probably isn't a big deal to a very large number of people, but is an advantage anyway, as it offers increased flexibility. It's also a single slot card, and can be used in an SLI rig.
The x850xt's real advantage comes in its ability to overclock much better than the 7600GT will. These things are supposed to scale very well, especially if you slap a third party heatsink on like an ATI Silencer (which you may want to do anyway to keep the noise level down). You also get ATI's perceived image quality advantage. And from what I've seen, they cost a bit less (~$25), which will just about pay for an ATI Silencer over at ZipZoomFly

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So, end of story? If you're going to overclock, and can live without SM3.0, get the ATI. A good OC will give you great performance. If you intend to run at stock speeds and you need the dual-dvi or sli capabilities, the 7600GT is the card for you.