As with most things, it's a matter of trade offs.
nVidia has tensor and RTX units, but these occupy die space and spend power.
On a normal graphics card with it's own PCB, power delivery and a die that is only for the GPU, this doesn't matter much.
But consoles have an SoC, that share CPU, IO and GPU. If you spend die space on RTX units, you lose room for s compute units.
AMD's solution allows for enabling ray-tracing with minimal area used. It's performance is lower than nVidia's, but it's a trade-off.
Also consider, that nVidia doesn't have a GPU with an hardware scheduler and an advanced front-end, since Fermi.
This on PC is not very important, because users can just buy a faster CPU.
But on consoles, it's very important to maximize performance and optimization.
A few years back, in the days ofd the original Xbox, I heard a story that MS was not happy with their relation with nVidia.
Mostly due to prices for the GPUs for the console, especially after a process node reduction.
But the gist of the story was that nVidia is a somewhat difficult company to work with.
And matter of fact is that both Sony and MS had one console with a GPU from nVidia. Only One.
AMD/ATI has already participated on 3 consoles for MS and 2 for Sony. More if you consider the PS4 Pro and Xbox One X.
Another advantage of AMD is the X86 license. By having the same X86-64 arquitectures on consoles and PC, it facilitates porting between platforms.
This is why, in the last decade, we have seen a boom of many console franchises also being ported to PC, and PC franchises being ported to consoles.