If you don’t want proprietary drivers the choice is quite straightforward: AMD. The official drivers are open source.

As for my experience, I’ve had absolutely no problems in the last few years with AMD, but I have to admit that I have always been using an iGPU, which has always been good enough for my needs.

I used to have problems with Nvidia proprietary drivers, but that was at least a couple years ago, things might have changed. I’ve never had issues with the free unofficial drivers, besides worse performance.