Depending on the system XP and W7 will perform the same for AH. I can run AH the same in both XP and W7 but since W7 needs more RAM by default and unless trimmed will use more CPU by default (due to so many processes running) it depends on what the system specs are.
Also, by "the same" I mean it plays at the same Frame-rates with V-sync on in both OS's. In this case I stay 59-60FPS, but if I disabled it I would likely get higher FPS in XP, but playing with it disabled is a very bad idea.
The main problem AH had with Vista/W7 was being put in the C:\Program Files\HTC now it's just C:\HTC by default to rid of those troubles.