I’ve done both. It’s was very quick boarding on the bellissima in the Mediterranean because they do bring passengers on at each port. Btw, I think that port fees varied by port embarkation so see which port is easy to get to and have lower port fees. I also was on the meraviglia in the Caribbean.
I enjoyed both cruises but for a reason I can’t define, the edge goes to the Mediterranean maybe because it was my first cruise!