Basically youre right as far as different genres go. in an FPS you can turn 180 degrees within half a second or something like that. For these games a "slow" lcd-panel might not be the best choice. That is because if you change a pixel from white to black it takes some amount of time until that pixel is black on the screen. It has some "afterglow" (dunno the corrent word).These times are shorter on CRT-Displays then on LCS-Displays. So, when much is going on on the screen, a CRT-Dispaly might work better.
But if AH works for you, then AH2 will too.
I would say there is no difference from AH2 to AH, because its the same flightsim. Rollrate or elevator authority could change, and then you would have such a problem. But I dont think FM will change that much.