I spend a lot of time on the boat in both the BVI and Antigua and, over the years, have come to enjoy Antigua more and more while developments in the BVI have me spending less time there each year. This is from a sailing and cruising point of view, things when land-based are a bit different. Since I don't know if you plan on being land-based or boat-based I'll pretend that you will be boat-based and answer accordingly.

In the BVI moorings balls are to be found everywhere and most anchorages have facilities for food and drink ashore with easy access to boaters. Antigua has only one anchorage with free mooring balls that I can think of (which is off Green Island) and you will be anchoring most of time. Many anchorages have nothing ashore. Others have more selection ashore than you can find in the BVI (English Harbour, Falmouth Harbour, Jolly Harbour for example). Sailing conditions are a bit more spirited and challenging than in the BVI. The island is bigger around than the BVI and with 365 beaches there's a lot of sand to see

I've found that the attitude (towards tourists) from the people you meet in Antigua has improved significantly and they are much more open and friendly to foreigners/visitors/tourists than 10 years ago. I cannot state that for the BVI.