Here's an excellent rundown of this ID problem from the Cornell Lab's web
Worth bookmarking or printing out to have on hand if you see one of these
guys and aren't sure which species it is.
Note that the sole absolute diagnostic is the thickness of the legs, if
you get a good view of them. Sharpies have toothpick legs, Coops' have
thick, sturdy ones. If you can't see them, you have to check other,
subtler differences and add them up to come to your conclusion. And most of
them aren't always easily seen, either!
Note also that the big female Sharpies are very nearly as large as the
little male Coops, so size is not a good way to tell which one you're
looking at. (There's no discernible difference in plumage between male and
female in either species.)