I run the game maxxed out with AA and everything on a lesser card than some mentioned above. It's not the lack of horsepower, its just drivers/software that needs to be worked on. There's no point discussing AA being the killer etc, its just drivers/game optimization.
If you're running a low-medium range card then sure switch off AA and pick up a few extra FPS, but if you have a $400 card and are getting slow downs its obviously not for lack of power to run the game with AA, its just driver/game issues. Check and make sure every driver on your computer is up to date and windows is up to date and if it is still an issue then hope that Nvidia/AMD will release updated drivers for CoH2.
Except 7990 or Titans, I really wonder which card can do that performance in this stage