Yes and no. "by a large margin" is open to interpretation.
In number of cases 65% of cases are vaccinated people, but if you prorate it to the number of people vaccinated vs non, you still have a 4x higher chance of catching if unvaccinated. We will see if this evolves, but that was the situation up to Dec 17th
edit after I originally posted. The under 12s are skewing the numbers. They are a big percentage of the cases and a big percentage unvaccinated. Your statement is accurate for the older age groups.
Cloudsurf posted a tidbit that double vaccinated that had a break through infection developed a very high level of immunity. The study was at a small scale but if it pans out, great news. May make some heads explode if they need to get vaccinated to develop their natural immunity LOL.
This study of fully vaccinated health care workers examines antibody levels and variant cross-neutralization after COVID-19 breakthrough infection.
jamanetwork.com