Comment by timr

Parent is overstating the case. Neither infection nor vaccination provides sterilizing immunity [1], but the general reasons to prefer vaccination are (in order of descending quality of evidence & reasoning):

1) you probably haven't had all N strains yet.

2a) you likely haven't been infected with the ones that cause cancer, because they're relatively rare.

2b) ...that is especially true if you're young and not sexually active.

2) being infected with one strain does not provide sterilizing cross-immunity against the other strains.

3) even if you've been infected with a strain, some of the vaccines have been shown to prevent reinfection and reactivation better than natural infection alone.

4) in general, the vaccination-mediated immunity might last longer or be "stronger" than the natural version, since the vaccines are pretty immunogenic, and the viruses are not.

But for point 4, it's well-known that vaccine efficacy is lower for people who have already seroconverted (cf [1]), so there's clearly some amount of practical immunity provided by infection.

[1] The vaccines are roughly 90% effective for the major cancer-causing strains, but it's not a simple answer, and varies a lot by how you frame the question. See table 2 here: https://pmc.ncbi.nlm.nih.gov/articles/PMC8706722/

Also be sure to see table 4 if you're a man. The data for biological men and women are surprisingly different!