A vaccine usually gives better immunity over natural exposure especially for respiratory tract diseases as the lungs/ airways give poor natural immune responses. In terms of antigens, if it's an attenuated (or dead) virus the antigen is the same as natural, in the case for SC2 all the approved or nearly so vaccines use encoded pieces of the spike protein either via mRNA (Pfizer/ Moderna) or it being stuck into a different viral vector (A-ZOxford/ Sputnik) which is deliberately designed and won't (necessarily) be the specific antigen segment(s) targeted naturally.
SC2 is not a slow evolver, it's a fast one. It's a ssRNA virus, they all evolve rapidly because ssRNA is inherently the most unstable genetic option- single stranded gives no redundancy, RNA is less stable than DNA. It isn't as fast evolving as its relative ssRNA virus influenza, but flu is an extreme outlier there due to the way it is assembled in segments. Spike had no known mutations for months, but the new UK variant has (iirc) 8 substitutions from the original spike, which probably explains its extra infectiousness. Since all the vaccines target spike due to it previously being stable mutations there are a big deal as they potentially reduce the induced immunity.
'Natural' herd immunity is not a viable strategy, but not because it's a slow infector. It isn't as fast as measles but again, that's a big outlier in terms of infectivity. Bit simplistic but, herd immunity works when the virus cannot find enough non immune people to continue spreading, so the R number drops, eventually below 1. That's ~65 to 70% for standard SC2, and probably a bit more for the new strain. IIRC the immunity for common cold coronaviruses lasts a few years, so using that as an estimate if something like 25% of the population was infected per year you'd never actually reach herd immunity levels because you'd not reach 75% immunity- those infected in the first year would be losing immunity as those infected in the 3rd were gaining it. That makes sense, because most viruses don't 'die out' naturally due to herd immunity, even those with 'permanent' immunity like chicken pox or mumps. They percolate in the background, occasionally flaring up when immunity levels drop enough. Vaccine based immunity should last a bit longer than natural since the immune response is stronger, but how long and how consistently long is a very open question; but with vaccines you can at least theoretically get to (effectively) 100% immunity (in this case the highest possible seems to be 95%) per smallpox and nearly polio.