I've been told from a reliable source that white shrimps and brown shrimps are anatomically indistinguishable other than their different mating period. (and their color obviously)
There is a way to tell them apart besides the color. In fact white shrimp and inshore brownies are hard to tell apart color wise and even more so after peeled. And there are more than one type of brown shrimp. From my exeperience in the seafood business and what all others say in the business, brown shrimp have thicker shells, are easier to peel, and the meat is firmer. Brown shrimp are also more dense and will be heavier given the same size brown versus white.