Recent observational study: https://pubmed.ncbi.nlm.nih.gov/34724027/
Conclusions and relevance: Prior SARS-CoV-2 infection was associated with a statistically significantly lower risk for breakthrough infection among individuals receiving the BNT162b2 or mRNA-1273 vaccines in Qatar between December 21, 2020, and September 19, 2021. The observational study design precludes direct comparisons of infection risk between the 2 vaccines.
Discussion concerning the question in the title.