With Doom 3 we see straight away that the open-source AMD Radeon Linux graphics driver has come along way compared to where it was just a few months ago when Ubuntu 13.10 shipped in October. Moving from Mesa 9.2 to Mesa 10.1-devel was a huge performance win as was the Linux kernel upgrade to 3.13 with Radeon DPM enabled by default and the important render back-end fix.
While the open-source Radeon driver has matured a lot, its performance is still far behind the Catalyst closed-source Linux graphics driver. For demanding OpenGL workloads the frame-rate performance is only about half of the Catalyst driver.
With the defunct Nexuiz game, the RadeonSI performance with Mesa 10.1-devel and Linux 3.13 kernel is actually close to the Catalyst driver.