Just thought I mention the recent AMDGPU-PRO BETA driver that has a DKMS module that works with 16.04 Ubuntu releases (sorry no source for ARCH or any other atm due to BETA) makes a great difference, even out does fglrx.
Games I have tested so far that really put AMD cards to the test are: Warthunder and Dying Light, the first game is notorious for being extremely pro NVIDIA when it comes to performance tweaks (Gaijin really don't like AMD).
Now there are some things to consider, I'm using a R9 390X. The drivers appear to work on 7700 series and up cards, ignore the list AMD gives on site, that is 'what we have bothered testing so far' list and isn't representative of what cards may actually work fine with driver.
Essentially all GCN 1.1/1.2 cards SHOULD work with it.
Very IMPORTANT, you will need AMDGPU and CIK enabled in the kernel, my Ubuntu 16 MATE had CIK support disabled for some reason, so I had to recompile my kernel from stretch, as such I decided to compile Kernel 4.6 and I suggest everyone else to do the same to ensure they get recent patches (haven't tested 4.7rc's atm).
Here is a kernel building guide I used (https://wiki.ubuntu.com/KernelTeam/GitKernelBuild) just grab the source tarballs from official sites.
Anyway with radeon/amdgpu open driver I was getting 10-28fps in Warthunder with LOW as can be settings, while with AMDGPU-PRO I was able to achieve 50-70fps with medium-high settings at 4k!, thats with grass slide halfway too! I did notice that ground forces was more smoother then flying, but perhaps thats because flying on ground force maps stresses the GPU more vs just Air maps.
Dying Light at 4k appeared playable but will likely need some settings adjusted to get the best out of it, I also only had the demo so no idea if full version works better. Next on my test list will likely be Mordor or something.
Note about Vulkan, this component must be installed separately and fetched from the LunarG website. Its mostly pain free process and AMD provides instructions (you will need an account to login and download it I believe). Be sure to build and run the provided cube/trig tests to ensure you have Vulkan installed correctly.
I hope all this can be made a little easier to do in the future, having CIK disabled in my kernel config really messed me up for a good few hours as it forced my monitor into 1024x768 mode and caused crashing.