When I was due for an upgrade, I chose low to mid-range AMD card supported by new open source drivers on Linux. Literally 0 issues and nothing to install. Pure plug and play. Am not sure about performance gain or loss since I haven't touched Windows for a while.

With nVidia it was annoying and occasionally painful experience. Annoying because you had to install drivers and sometimes nVidia stops supporting your card, so you have to chase older drivers which might not be supported on your OS now, etc. On occasion those drivers would break after update and my system simply won't start and I would have to revert to Nouveau to get any work done. Didn't happen often, but enough to be annoying and the fact they chose the worst moment to break made it painful.

One thing I really liked about AMD cards that makes me happy I have one right now is output ports. AMD seems to be pushing more modern connectors than nVidia. In same generation I had nVidia with HDMI and VGA, while AMD pushed for HDMI and DVI, which can push analog but is at the same time digital. Since I like having two displays AMD's choice was better. These days I use fiber optic HDMI cable for TV and having card with 3 digital connectors is very nice. Pushing 3 displays with nVidia card at the time was problematic if impossible. My solution was usually to have built-in Intel card push TV HDMI and other two displays were on nVidia, but since nVidia likes stepping over open GL libraries there was no hardware acceleration for Intel.

Granted this is all thing of a past but I don't think I'll switch from AMD anytime soon as they seem set on providing good quality open source drivers.