To clarify for the purpose of answering OPs question. The quality will be the same because it's the same code in both cases. But the performance, as in how many FPS, you get will most often differ.

GSync only works on Nvidia cards and GSync monitors

I have a Freesync monitor (MSI) with an Nvidia RTX 3060, and Nvidia control panel gives me the option to "enable support for unverified displays" or something. Works just fine for me?

Couldn't there be a difference between demonising algorithms if those are baked in the drivers?

To add to this, most gpu reviews will now have two sets of benchmarks, one with ray tracing and one without. You can see the gap in raytracing performance at each price point narrowing considerably over the years as amd catches up. It also narrows further at higher resolutions (since the price equivalent amd options tend to have higher raw performance and more memory which becomes increasingly important at higher resolutions). Right now all else being equal at most price points you'll see amd with a lead in non raytracing performance, and Nvidia with a lead in ray tracing performance. In addition to considering target resolution, which card is winning out can also be very variable per game, so if you have a particular game in mind, would see if there is a benchmark for that game so you would know what to expect with different cards and see what makes the most sense with your targeted performance, budget, and priorities.

And to clarify for OP, when I say raytracing performance, I mean the fps with raytracing turned on. Visually it will appear the same in each particular game no matter what gpu you're using, since it's the game that implements the ray tracing. The one exception I know of in terms of actual quality right now is "ray reconstruction", a part of dlss, that will only work on Nvidia chips, and that they claim improves the noise between individual rays better than traditional de noisiers through use of AI. Theoretically there should be other ways to reduce noise at a performance cost too, so in the end it does come down to performance and game by game implementation again. Not a lot of games with this right now, I think cyber punk, portal 1, and control.

Especially since I use vr sometimes, I tend to favor the raw power at the price point more to get the best resolutions and frame rates. If you're favoring just a great picture at lower resolutions like 1080p there starts to be diminishing returns (is 180 fps really a better experience than 120 fps?) in favoring non ray tracing performance, maybe making a less raw performance Nvidia card even more of a consideration if you feel the non raytracing performance is good enough. And then if money is no object of course, Nvidia has the best performing gpu overall in all aspects at the extreme high price end (4090), with no equivalent amd option at that level.

Also dlss vs fsr needs to be considered. Fsr being not as far along as dlss. This would be more important at the lower end though (except in the case of ray reconstruction), higher end gpus likely won't need to rely on these technologies to achieve good fps with current games. Hopefully fsr continues to improve and become a more widespread option. Amd is also working on fluid motion frames at the driver level, which may allow a similar effect to fsr 3 even if not implemented specifically by the game.

I find it odd that people say "No, Nvidia is better"

I'd assume that by better, they mean the performance, I'm which Nvidia is definitely better. They've been doing it for longer and at this point. Account for the number of years in the game and they're pretty equal. 20 series Ray Tracing is a joke.

The majority of people aren't bothering with RT anyway.