A growing body of evidence suggests that fully vaccinated people are less likely to have asymptomatic infection and potentially less likely to transmit SARS-CoV-2 to others. However, further investigation is ongoing.
The data we have are limited and mostly indirect at this point, but there are no data that I have seen to indicate the converse. It would be very much contrary to expectation that a vaccine that is highly effective at preventing disease would not also be effective at significantly reducing transmission.