I am having the same issue. In my case I "upgraded" from a HD 5850 to the HD 7870 and I don't see much of the performance increase. I am very disapointed.
With my old card I was running on ultra and getting 20 - 30 fps in populated areas. My screen resolution is set to 1929x1200. No addons. With the 7870 I am getting basically the same fps.
I uninstalled the previous drivers and installed the latest from the AMD website. I have not tried yet the beta drivers but for what I read it will improve performance on new games not for this old game.
Reducing my WoW settings should not be the solution. I am pretty sure this is a very good card but the drivers are not optimized for old games
My system specifications are on my signature. Any help will be appreciated. Thanks
Intel Core i5-655K @4.8 GHz, Biostar TB55HD, 16 GB ram @ 1600, AMD Radeon HD 7870, 256 GB SSD, 2 TB HDD, Corsair H70, Thermaltake TR2-700W, Windows 7 Professional x64