I have the same problem with my ATI graphics, see
Post#455756 for a more detailed description.
In my case, glxgears and other games work fine, but DomIII somehow still uses the wrong software libraries (MESA) and hence is real slow. So it is either the fault of the ATI drivers or the distribution. What Linux distribution are you using? And please post if you find a solution (I have given up for now)!
Interestingly, Dom2 does still runs very fast...