Nvidia spends more money on marketing, developers, tooling, documentation, infrastructure, and publishing high quality, usable libraries for GPU numerical computing. They have been doing this for years (CUDA is +10 years old) and are very good at it, while HIP/HCC are just barely usable. This is basically all it comes down to, in a nutshell. I want to be clear that none of this is trivial in any sense; delivering a usable GPGPU software stack is extremely difficult work, and Nvidia is simply
miles ahead of AMD in nearly every way, except the fact ROCm and the AMDKFD driver are going upstream to Linux. AMD is of course also a smaller company than Nvidia, as well, so their resources are more limited.
Here's the thing: In reality, it doesn't matter if a Radeon VII or Vega64 has better theoretical TFLOPs than a 1080 Ti or whatever if the card runs 50W hotter(!!!) and the software is bad enough it runs at 1/2 the performance of the competitor. 50W hotter at a 10% perf loss and a 40% decrease in price is attractive. Hotter at 1/2 the perf, is a non-starter (almost entirely ignoring price factors). Free drivers do not make up for this. DL is a fast enough field that, for most practitioners, your time is better served as an enthusiast/participant by just paying the extra upcharge on an NVidia card and getting on with your life, so you can actually train models and do your work.
There is only one viable solution if you want to "do your work" today -- not for better, and almost certainly for worst. Ceterum censeo.
DL moves fast enough that it's always possible for new frameworks to come around, so perhaps a competitor with a multi-vendor design, from the ground up, can break though. But then you have to ask whether a lot of these frameworks can even succeed/tread water in such an environment without Google/Facebook propping them up, which is a separate problem... And before that, AMD has to make sure HIP/HCC have to work reliably, every time, everywhere, and they have the libraries to back it up. I'm hoping the succeed at this.