First of all OpenGL rendering performance is lower with Nvidia cards as well. But AMD has got some extra bugs in there. It begins with the wrong initialisation, the later result are flickering textures. There is a hack that lets those go away: press while the menu (and not inside a level) Alt+Enter twice or use gfxRestart() as console command. You can switch to OpenGL on Win as well using "gfx_iAPI = 1", then restart the the engine or the game. One extra curious thing is when you have got a Crossfire setup. On Win using D3D the performance increase is absolutely minimal, but when set to OpenGL then it drops massively. On Linux Crossfire has basically no impact for most games, but you can see the performance drop there as well. HD 5670 - most likely driver 12.11 beta but the driver version is not important for this issue:
Btw. i see it as very bad joke when SS3 is mentioned in the changelog of a beta driver and the bug is still there!