Linux Gaming

Nvidia drivers have (slightly) more timely support for the latest cards, and more mature support for non-3D uses of the GPU, especially scientific computing. To a large extent they are the same code as the Windows drivers, and that has positives in terms of breadth and maturity of support.

For everything else, the AMD drivers are better. Because they are a separate codebase from the Windows drivers, and are part of the de-facto Linux GPU driver stack Mesa, they integrate much better into the overall Linux experience, especially around support for Wayland. Unless you have an absolutely bleeding-edge card, they "just work" more often than the Nvidia drivers. If you like doing serious tinkering on your Linux system, then the AMD drivers being fully integrated and having the source available is a major win. Also, it used to be that the Nvidia drivers did a much better job of squeezing performance out of the hardware, but today there's very little in it, and the AMD drivers might even be a little more efficient.

I've got both AMD and Nvidia GPUs currently in different machines, and I much prefer the Linux experience with AMD. I don't think I'll be buying another Nvidia GPU unless the driver situation changes significantly.

FWIW I don't stream so I can't comment on the exact situation, but I have used the video encode hardware on AMD cards via VAAPI and it was competent and much faster than x264/x265 on the CPU. I think OBS has a plugin to use VAAPI (which is the "standard" Linux video decode/encode acceleration interface that everyone but Nvidia supports).