Phoronix published a review on the Radeon Linux 4.6 + Mesa 11.3 vs. NVIDIA Linux Performance & Perf-Per-Watt A quote from the article:

Last week I published a 16-way NVIDIA GeForce performance comparison on Linux looking at the OpenGL performance evolution from the GeForce 9800GTX to the GeForce GTX 980 Ti / TITAN X, in getting ready to compare the long-term NVIDIA Linux performance to Pascal. This week I've done similar tests on the AMD Radeon side and compared these OpenGL performance and power consumption / performance-per-Watt numbers to NVIDIA.

For this round of testing I was using the very latest open-source AMD support: the Linux 4.6 kernel and Mesa 11.3-devel from this week. The Mesa 11.3-dev deployment was via the Padoka PPA atop Ubuntu 16.04 x86_64. The DDX drivers were also up to date for the testing process via the Padoka archive. The rest of the Ubuntu 16.04 stack with Unity 7.4, X.Org Server 1.18.3, GCC 5.3.1, etc, were maintained the same as last week's NVIDIA GeForce test results done using the 364.19 proprietary driver. The same test system was obviously used with the Xeon E3-1280 v5 Skylake CPU, MSI C236A Workstation motherboard, 16GB of DDR4-2133 EUDIMM memory, and 120GB Samsung 850 EVO SSD.

 Radeon Linux 4.6 + Mesa 11.3 vs. NVIDIA Linux Performance & Perf-Per-Watt @ Phoronix