If you want to follow the advancement of Linux graphics stack (while having reasonable graphic performance), AMD is your choice. This is where the exciting new stuff, like Wayland, DRI3 etc. happens. The NVIDIA proprietary driver indeed has amazing performance, but is falling behind on this regard.
AMD's Linux team is in the middle of a big push to modernize the driver and software stack. It seems they consider it a mostly working preliminary version.
You can choose-your-own-adventure with the totally open amdgpu+mesa stack or use the proprietary AMDGPU-PRO. You can follow development of the open source parts on this mailing list:
https://lists.freedesktop.org/archives/amd-gfx/
I do agree with others that NVIDIA is a better choice if you want something that just works and you don't care about proprietary vs. open source.
In terms of stability, the proprietary nvidia drivers are simply the best, and gave me significantly less issues. For my daily workstation I even ended up replacing my (expensive) AMD card for an nvidia one because the desktop environment felt like it was running less than 10 fps, and it triggered me to no end.
Even if AMD gets equal or even better performance than nvidia in gaming environments, I am not willing to compromise the desktop for that.
If you don't mind using the closed-souce nvidia driver, I strongly suggest nvidia.
I bought an nVidia card and didn't have to touch anything and it's completely stable (in the same exact PCI slot).
I might try AMD again in a year or two as I prefer their model of actually supporting and writing open source drivers in contrast to the scummy nVidia whose cards now require a signed firmware that they won't release to the open source community after we got the reverse engineered open source drivers (well, they did release one now for the 9xx series after they released the 10xx series).