Good review, I've wanted to see some results on this for a while. I was getting performance drops in Riddick and UT2004 on my 7800 GTs that were big enough to be noticeable during normal gameplay (without doing any benchmarks) when the HQ mode was turned on. I just stayed away from AF in these games and stuck with quality mode (they look mostly identical without AF), as the quality mode AF looks worse than having no AF at all in my opinion.
However, Nvidia's HQ mode doesn't remove the shimmering altogether; it's definitely still there in some games. After doing some comparisons with my new card I think Nvidia's AF on HQ mode shimmers a little less than ATI's HQ AF, especially with the LOD clamp enabled. Both look far better than the 7 series' quality mode AF, but Nvidia has a noticeable advantage with HQ and LOD clamp both on. It's a pity that the performance hit for HQ is so significant and the only alternative is the quality mode AF that looks like crap. As far as I know, there is no way to get completely perfect AF on any of the modern cards.
It might also be interesting to see how the Geforce 6 series cards stack up. Although I never did any direct comparisons, my old 6800 GT shimmered a lot less than the 7800 GTs I was using until recently. I never really noticed it unless I was specifically looking for it on the 6800 GT, but it stuck out like a sore thumb immediately when I first started a game with the 7800s.
On a note about the shimmering itself, for those of you who can't see it, look for a game with a large room that has both simple level geometry and high resolution textures, particularly grid-like ones such as square floor tiles, run it at least 1600x1200 if possible and use 16x AF. I think these are the conditions under which the effect is most apparent.