Something I still fail to understand is why people keep trying to compare DLSS vs FSR.
It's like comparing a F1 car with a street legal Volkswagen.
Of course DLSS is better. It SHOULD be better, any time and under any circumstance. It relies on somewhat expensive hardware (RTX only with Tensor Cores), and on heavily trained neural networks (a work that it's also needed, but hopefully it's done, at least for now, by NVidia themselves).
FSR, on the other hand, is an universal technology, open source and one that doesn't need any special hardware to run. Of course it's less advanced by it's own nature, and it SHOULD be slightly worse on any likely scenario.
Is like asking if a F1 is a better car than a Volkswagen Arteon. A F1 is faster, yes, and much more maneuverable. That doesn't mean that everyone should rush to their car dealers to get a F1 single seater.
The question is not if DLSS is better or not than FSR. It is better, by it's own design.
The real question is if FSR is good enough to be used on all those hardware that is not able to run DLSS (AMD, Intel, and older nVidia own GPUs), and if it's relative quality and universal availability will make up in the long run for the superior, yet more expensive DLSS alternative.
This last question, only time will tell.
Maybe the two can coexist; but I've always preferred open standards than propiertary solutions, and AMD solution wins here hands down. FSR needs to prove that it is good enough for it to become dominant, though. Even if everyone and their mother should be aware that, on any case, it won't be able to match DLSS quality most of the time (or any time for that matter).
For now, the results are promising though. FSR is, right now on it's first iteration, quite better than DLSS was on 1.0, even being designed under a "worse" technology base. It works quite nice on most if not all recent non-RTX GPUs out there. And it should improve even more with time...