The big difference is that the copies cannot make copies of themselves (they are only partial copies) so the viral load does not grow geometrically within your body.
Again: if the small viral load of a vaccine makes a person sick for a week, that person likely has a higher risk for severe illness from the (much larger) live viral load from a full infection.
Science does not yet understand why some people have more severe COVID illness than others, but it is an observed fact that some do. In some cases, even if they are otherwise fit and healthy.
That you are used as the factory for the protein with mRNA doesn't make a big difference IMHO.
I'd beg to differ, or at least make a slight distinction. The mRNA vaccine targets the spike protein specifically, which is the important target in the virus, at least now, but not the only one. The actual virus is more complex than that, and it can mutate. From this POV natural immunity is better. But natural infection obviously comes with the downside of added risks (depending on your immune system) and it's tough to guess how you'll react the first time (although you can make educated guesses) you get infected. Later infections will be milder though. And a clear upside being not having to run for jabs a couple of times per year.
Whoa, hold on there buddy.
You might want to look up the difference between mRNA vaccines and traditional ones.