Actually, AMD does WoW better than Nvidia, hell CF worked for a long time with it while SLI has been forever borked. I played it with cards from both, since 2004 (or w/e it launched in Europe), and both have been more than fine. As others have said, this is about CPU as well as the simple fact that the game is ancient and has issues with optimization due to it (and just being an MMO..)
The thing is, you gotta play with the settings and do some tests, I know last time I played it some settings made the game come to a crawl but with minor tweaks it was smooth as butter. In particular also, some zones are annoyingly laggy, like Felwood. There's a lot you can do, but if you just push sliders to max and hope for the best - yeah, that's not gonna work.
Because some people actually play games instead of just benchmark them.
Never seen CF work very well with it - dunno about more recently as I don't know anyone who has played it on CF since the 6000 series but a few years back it was causing stuff like texture corruption issues and doesn't work in window mode with CF which a lot of WoW players use for access to helper/stats programs, voice comms, etc.