With Doom 3 there isn't too much to look at. The R600 Gallium3D performance really didn't change for the tested GPUs between Mesa 9.2.1 and 10.1-devel nor was there any breakthrough performance boosts between Linux 3.11 and 3.13 on the DRM side for these older HD 4000/5000/6000 series graphics cards. The open-source AMD driver was running just under 50% the speed of the Catalyst driver for this testing.
With the Nexuiz results the data is more interesting as we see some performance improvements out of the newer Mesa code as well as when upgrading to the latest Linux kernel. For the Radeon HD 5830 with Mesa 10.1-devel + Linux 3.13 the performance now matches the Catalyst driver! For the Radeon HD 6870 the performance in this most up to date driver configuration exceeds Catalyst! The Radeon HD 6950 performance though is still a bit behind Catalyst. Sadly we have no Catalyst HD 4870 numbers due to AMD no longer maintaining the legacy Catalyst driver.