Prior research generally finds that the Pfizer-BioNTech (BNT162b2) and Moderna (mRNA1273) COVID-19 vaccines provide similar protection against mortality, sometimes with a Moderna advantage due to slower waning. However, most comparisons do not address selection effects for those who are vaccinated and with which vaccine. We report evidence on large selection effects, and use a novel method to control for these effects. Instead of directly studying COVID-19 mortality, we study the COVID-19 excess mortality percentage (CEMP), defined as the COVID-19 deaths divided by non-COVID-19 natural deaths for the same population, converted to a percentage. The CEMP measure uses non-COVID-19 natural deaths to proxy for population health and control for selection effects. We report the relative mortality risk (RMR) for each vaccine relative to the unvaccinated population and to the other vaccine, using linked mortality and vaccination records for all adults in Milwaukee County, Wisconsin, from 1 April 2021 through 30 June 2022. For two-dose vaccinees aged 60+, RMRs for Pfizer vaccinees were consistently over twice those for Moderna, and averaged 248% of Moderna (95% CI = 175%,353%). In the Omicron period, Pfizer RMR was 57% versus 23% for Moderna. Both vaccines demonstrated waning of two-dose effectiveness over time, especially for ages 60+. For booster recipients, the Pfizer–Moderna gap is much smaller and statistically insignificant. A possible explanation for the Moderna advantage for older persons is the higher Moderna dose of 100 μg, versus 30 μg for Pfizer. Younger persons (aged 18–59) were well-protected against death by two doses of either vaccine, and highly protected by three doses (no deaths among over 100,000 vaccinees). These results support the importance of a booster dose for ages 60+, especially for Pfizer recipients. They suggest, but do not prove, that a larger vaccine dose may be appropriate for older persons than for younger persons.