We've done the three night twice, the 7-night once, and are planning a 4-night. We thoroughly enjoyed the shorter cruises and decided we actually prefer them to the longer ones. By staying on the ship in Nassau, felt like we got to fully experience everything on the ship that we wanted to. We used the pools, aquaduck, rainforest room, ate dinner in each restaurant, enjoyed pirate night, went to character meet and greets, did some of the scheduled entertainment, and saw all three main shows. And best of all,
Castaway Cay was amazing.
I really don't feel like you are migssing out. In contrast, I felt like the 7-night was a lot of repetition (same restaurants, same characters, same bingo/trivia, same pools/slides over and over), the additional shows were not as good as the three main shows, and none of the port stops were as fun as Castaway Cay.
But we're not typical. Most people here will tell you longer is better. I think it is unusual to find people like me for whom longer was not as good. But I do think there are plenty of people who think 3 days is a good vacation.