I'm not an expert in the field and I'm not going to say anything about end user experience^, however what I keep hearing from my professors and PhD friends doing research at my university on high-performance parallel applications on clusters of GPUs is that AMD GPUs usually have more raw performance (as in, reported performance) but nVidia GPUs have more control and better drivers. This means that on common benchmarks for high-performance computing (distribution of bandwidth, FLOPS, etc etc) nVidias still seem to get the advantage because it's just easier to squeeze more performance out of them compared to AMD ones. Also parallel algorithms are apparently easier to handle on the former rather than the latter.
ps: this is all from hearsay and unofficial conversations, I don't have sources to validate nor disprove any of the claims I made, sorry.
^ I use an nvidia and an intel integrated gpu on my linux desktop and laptop respectively and never had problems with either, just to note, I have no AMD experience.