Nvidia has had 3D capabilites with their 3D Vision technology for some time now, but only recently released 3D Vision 2 with a few improvements. AMD on the other hand is fairly new to the 3D world, and their HD3D technology is actually only natively supported in 3 or 4 games right now including Dirt 3 and Deus Ex Human Revolution. For every other game, it actually needs to rely on third party drivers in the form of IZ3D and Tridef 3D.
Because Nvidia uses a more closed system for their 3D tech, they are able to keep tight control over how it all works and as such it seems to generally work better and in more games than HD3D. The downside, though, is that the 3D kits (3D Vision certified monitor and glasses) are quite expensive. AMD's more open 3D platform has the benefit in being able to use just about any 3D monitor and compatible glasses, many of which are from Samsung. They can be bought for fairly cheap too, as little as $350. The downside, of course, is that besides the few native HD3D games out there, how well it works relies on 3rd parties.
Now for the specifics, I'm going to have to direct you to a couple of articles. In TechReport.com's recent PC gaming in 3D stereo: 3D Vision 2 vs. HD3D, they cover everything from specifics about each 3D technology, supported hardware, and how to set it up as well as some benchmarks about the impact on performance. The only negative to this article is that they cover only a few games.
For another look at supported games and benchmarks, you'll want to check out Tomshardware.com's Stereo Shoot-Out: Nvidia's New 3D Vision 2 Vs. AMD's HD3D. This article covers many similar aspects to TechReport's, but has more games covered.
Tomshardware.com also posted an article that is a fantastic look at compatibility with 18 popular games, Nvidia 3D Vision Vs. AMD HD3D: 18 Games, Evaluated. The absolute coolest part about this is the images that let you see the 3D effect for yourself. Like this one:
|Cross your eyes until there is a single central image, then wait for your eyes to focus on it.|