The main differences between a Cooper's and Sharp-shinned I have found that birders go by are:
-Size: Cooper's hawks are larger and bulkier than Sharp-shinned hawks (be careful not to get that mixed with the dimorphism in size between the males and females of the species: females are larger).
-Tails: A Cooper's hawk has a round end to its tail, whil a sharp-shinned has a straight-edged square tail. As the picture above in the post, all the feathers on this hawk's tail are the same length, making it a straight square edge, which for me is good evidence it's a Sharp-shinned.
-Age: Juvenile of both species are mottled brown and streaky with strong brown streaks on white breasts. When they get their adult plumage, they have orange breasts with more of a slate bluish gray body.
-Prey: I think you could assume that a Cooper's hawk would tend to go for larger prey than a sharp shinned.
-Legs: A Sharp-Shinned hawk, as for its name, has long skinny legs with very long toes, and a Cooper's hawk has shorter legs.
Hope it helps. These are the easiest points you could go by for a sitting / perched hawk to identify. Correct me if I've made any mistakes!!!
thanks!
James