Afaik Blender since 3.0 does not support OpenCL anymore and AMD rendering uses HIP instead. I have not found any information about dramatic performance differences, though CPU rendering does seem to be somewhat faster on Linux - but more like 10% faster and the amount of computation practically done on the CPU is not that big.
Also this represents the biggest headache in Linux, lots of gamers insist they can only use Nvidia cards. Nvidia treats linux as an afterthought as best or deliberately sabotages things at worse.
Personally I use NVidia because of CUDA, gaming is an afterthought. I wish CUDA just fucked off and we got some universal compute API instead, because that's what would reduce the NVidia stranglehold on the market, perhaps OneAPI is going to catch on at some point, but at this moment those options are not practical.