We have both in our area and I have a very hard time telling them apart. I mostly just go Cliff Clavin on the matter and act like I am sure of the identification I just made...

The only things I've ever been told or read that would work are the size, Cooper's being slightly larger and the body shape. If it is one width from head to tail, it is probably a Cooper's. If it tapers back a little from the head to the tail, it is probably a sharp-shinned. Most of the time, you don't have a frame of reference for size, so that one isn't much help. And the body shape can be hard to see from many angles, so that one frequently doesn't work. Again, I defer to the Cliff Clavin approach...