AMD doesn't have a closed kernel component anymore. They do still have a userspace component, but most people use the free 3d acceleration instead, written with NDA-free documentation provided by AMD, with the help of AMD employees. This covers hardware up to their current generation, providing OpenGL 4.5 and Vulkan. Its performance is not as good as the Windows drivers, but good enough enough for most games out there.
Thanks to this, their hardware just works out of the box on any distribution that's not years behind.
As you don't even need to play games, I believe AMD is the better option here.
I just switched from AMD to NVidia because of driver issue. I run Arch Linux, and my experience is that installing NVidia drivers is miles ahead of AMD.
I run Arch and amdgpu was installed as a kernel driver out of the box. If you have an RX GPU, or any other one supported by the new drivers, you're going to have a great time.
I have experience with NVIDIA and AMD GPUs on Linux-systems and my experience with AMD was vastly superior. The difference was so significant that I rule out buying a NVIDIA card.
Thanks to this, their hardware just works out of the box on any distribution that's not years behind.
As you don't even need to play games, I believe AMD is the better option here.