It's Really Worthwhile For AMDGPU Users On Ubuntu 16.04 To Upgrade Their Kernel, Mesa
These are some fresh results with a Radeon R9 Fury when comparing the current packages on Ubuntu 16.04 LTS with Linux 4.4 and Mesa 11.2 versus the current development code with Mesa 12.1-devel and the Linux 4.8 kernel. Nothing else was changed during the testing process.
Before even talking performance, by upgrading your open-source driver stack you now have OpenGL 4.3 for AMDGPU/Radeon on GCN GPUs rather than OpenGL 4.1 as the version when Ubuntu 16.04 shipped.
You should find near universally that upgrading your kernel and Mesa will mean big performance wins when using the open-source AMD Linux driver.
With some Linux games, we are talking very big performance differences.
You can see more benchmark results via this OpenBenchmarking.org result file.
This kernel and Mesa version will end up in Ubuntu 16.10 come October, but by then will be Linux 4.9 and Mesa 12.2-dev as the latest upstream code for maximum performance potential...
The easiest path to upgrading your Ubuntu stable release is by using the Ubuntu mainline kernel packages and the Padoka PPA for not only providing newer Mesa but also LLVM snapshots for the AMDGPU back-end and other updated user-space components. While these tests were just with an R9 Fury on AMDGPU, for those with older GCN GPUs on the Radeon DRM driver you still should see nice performance boosts too if going for this route rather than just eating what is fed to you by the Ubuntu stable repository.