I found the open source driver situation to be quite good with AMD. I was able to play non-trivial games (TF2 and Dota2) and use two monitors quite well. In fact, the open source AMD drivers had better multi monitor support then either the proprietary or the community Nvidia drivers.
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.
