There are many kinds of ducks out there. I'm not clear if by Long Island ducks, you mean the kind you see in ponds or the ones you see frozen in supermarkets. Ducks, like chickens, are bred to be either egg layers or for meat. The duck in the movie, Babe, was an Indian Runner and is bred for egg laying. But there are breeds such as Aylesbury that are bred for meat and they get much bigger than the egg laying breeds. Mallards, which are the most common wild duck you see in the US, are more of a general breed so they are bigger than egg layers and smaller than meat breeds. It would not surprize me if they are raising Muskovies in the DR since they are tropical in origin and are very hearty.
If you are saying the duck in the stores are smaller, it could just be that their weight is the size that sells and that younger ducks sell better. The Pekin duck is also ready for market in just under two months, so it is prob smaller than other meat breeds.
Duck breast is my favorite cut of meat. I normally make a diagonal tic-tac-toe cut across the breast(with skin) grill it to render most of the fat, then finish it in the oven and serve it with bacon as a garnish.