I think it is very likely that vaccinated people are contracting COVID-19 less than unvaccinated people, but because most testing is done on symptomatic people, and the vaccine is known to reduce symptoms, the sampling bias is likely overstating the effect.
Vaccinations reduce your chance of getting infected and reduce the average duration of the infection. The combination of these two factors thus reduce the R value of covid in vaccinated populations when compared to unvaccinated populations with identical network topologies and behaviors.
"A growing body of evidence indicates that people fully vaccinated with an mRNA vaccine (Pfizer-BioNTech or Moderna) are less likely than unvaccinated persons to acquire SARS-CoV-2 or to transmit it to others."
