During AH2 beta, there were a ton of reports that any nvidia card would beat it's equivalent ATI competitor in framerate. HT got an ATI card to help boost the performance of AH2 on ATI cards, but since then I haven't heard ANY direct comparisons between equivalent nvidia and ati cards.
From what I've read in online reviews, the nvidia 6800GT beats the same-price ATI competitor in almost every single game, and that is one reason why I went with the 6800GT. AH2's previous affinity for nvidia cards is another, but I'm not sure that argument still holds up since I don't know of anyone who has done any direct comparisons. Maybe if someone asks skuzzy to do a comparo he could get HT to cough up the R&D cash to buy one of each so he could make a direct comparison, or maybe they could try to get some card manufacturers to cough up some freebies for development purposes, but otherwise good luck finding a direct comparison.
Part of the problem is that AH2 is configurable enough that it's very difficult to compare framerates and image quality reports from 2 different players. It's unlikely they'll be able to get their settings exactly the same, and there is no reliable way to get the exact same scene to allow for a benchmark session.
I suggest hitting
http://www.hardocp.com and
http://www.firingsquad.com to check out their comparison articles because both sites use at least one flightsim in their benchmarks in addition to the other shooter type games. From what I've read though, the $400ish 6800GT beats the $400 ati card right now.