I have the same problem when visiting Black Citadel .. my FPS goes down to below 10 and it becomes very hard to navigate inside the black citadel because everythings lags.
I have a pretty good computer.
Intel Core i7 CPU 950 @ 3.07Ghz(8 CPUs), ~3.1Ghz
12 288 MB RAM
NVIDIA GeForce GTX 560 Ti – 4050 MB (driver version 9.18.13.623)
Gaming experience really sucks in the Black Citadel.
Never experienced such issues with World Of Warcraft.