Out of the box, the end result is pretty similar for both systems...
The reason I knock HD3D is because when I first purchased my monitor, I was using 6950's. I could get HD3D through the HDMI port (all that was supported at the time. Displayport was added later). It looked pretty awesome in Crysis 2 and Metro 2033. Much better than I expected, which had me install some 470's I had in another system. It looked even better at 1080p.
Now, here is the dirty secret I've found in my experience and Nvidia has a built in tool in the Nvidia Control Panel with a list of compatibility; only about 20-30% of my games are fully 3D compatible out of the box. Most games that are reasonable require you to turn off shadows. Others may somewhat work and water effects are in 2D. And others have awful lighting issues.
Nvidia and AMD will recommend you turn those settings off, and then you may find 30-40% of the games out there will work, but losing shadows and see through water is kind of a deal breaker for me.
With the Helix mod, 3D Vision games can be fixed and there is an active community that has fixed a lot of games for us. They fix games that only have shadow issues, others with water issues, and light source issues. They have fixed a lot of games for us, and even gave a tool that can be used to fix a game yourself.
So instead of playing 20-30% of the games out there, with shadows off in half of them. I can play at least half the games out there if not more, and have all the effects work, though you are limited to Dx9.
http://helixmod.wikispot.org/gamelist
Every time I hear about someone who has some new info on AMD's HD3D, I load up Tridef and my 6950's, and the same issues remains. HD3D, like 3D Vision out of the box, has lots of compatibility issues with most games. 3D Vision has a mod community that can fix many of those issues. HD3D has no such community or hack. Apparently the problem is with how the settings are applied within their engines as Skyrim has fixes for both systems, only that HD3D's version is incomplete siting issues with how they handle 3D settings.
In some games HD3D will work great, such as Tomb Raider, as it is built to handled 3D, but most games are not.