To the GP's question, about whether catching something gives you better protection than having a vaccine, my (non-expert) expectation is that Covid is like the flu - my having had the flu won't give me protection for all future strains, so I'll keep on needing new vaccines periodically for those new strains.
It's also medically incorrect. When you get a vaccine you are literally getting a live virus injected into you. There's no difference for your immune system. One isn't "fake" and the other "natural". Period.
To your point, viruses mutate and so similar to the flu and flu vaccine, if COVID-19 continues to mutate in ways that are different enough we'll have to get new COVID shots which use modeling to predict the likely virulent strains. People that are aghast about this concept are not really understanding the new reality we're in. The only hope is that if enough people get vaccinated quickly enough, a new strain won't mutate and cause the vaccines to lose some effectiveness. I think that's a wildly naive hope, though and the best path forward is just treating this like a worse flu and moving on with our lives.
This is false for the mRNA vaccines according to the CDC:
mRNA vaccines do not use the live virus that causes COVID-19 and cannot cause infection with the virus that causes COVID-19 or other viruses.
https://www.cdc.gov/coronavirus/2019-ncov/vaccines/different...
In my previous comment I was unclear about what I was addressing and when, though ultimately the point is that this distinction of contracting a virus "naturally" versus "artificially" is not scientifically based. Applies to COVID-19 mRNA vaccines as well as flu vaccines.
If there's evidence to suggest otherwise though we should get that out there.
That has caused resistance among friends I know, who say that its not a real vaccine, since vaccines give you a small dose of a live virus to trigger one's immune response. Perhaps the mRNA injections should have used a different name to clear misconceptions.