What kind of AMD chipset are you running? The HD 7000 series for instance was released early in 2012 and only started having _experimental_ and incomplete OpenGL support a year later. The performance was atrocious even 18 months after release and it likely still is. In the end I bought an Nvidia card which worked fine out of the box.
AMD has been completely rewriting the drivers as free software. The 2d performance of the in-kernel drivers is now better than the proprietary driver for southern islands(HD7000). The 3d performance of the free driver is at about 50-70% of the proprietary for SI with linux 3.13, according to phoronix. The latest cards C.Islands use the same drivers as SI so the performance should be similar.
