IIRC vaccinated people spread smaller quantities of the virus, and the viral droplets they do spread tend to include antigens since their body is actively fighting the infection while they spread it... you know, because their system was primed for the fight thanks to the vaccine.

I think this Fridman podcast interview explored such things, either way it was quite informative on the subject:

https://www.youtube.com/watch?v=G433fa01oMU