BlackGoldAg2011 said:
Here's a study done one international travelers arriving in Qatar Feb-April of this year where everyone was quarantined and tested. The article and figures have some good data, but the TLDR is that it looks like immunity from natural infection is roughly 8% less than immunity from vaccination during that time period. So maybe slightly lower, but still very good based on the data.
https://jamanetwork.com/journals/jama/fullarticle/2781112
That is a PCR study where presumably many naturally immune people made it into the "vaccinated, no prior infection" group. Antibody testing studies are much more reliable as they can identify those with both natural nucleocapsid protein and vaccine spike protein.