We have both Sharp-shins and Cooper's in the woods next to our house, and we beleive the Cooper's is a resident, as it snatches a songbird off our feeder with some regularity.
Two features seem consistently helpful in telling them apart, at least to me. First is the tail, especially when perched. The tail on the sharpie tends to look square-cut, while the Cooper's looks a bit rounded. Sort of like the difference between a flat and filbert brush, if you're a painter. Second is the overall 'gestalt' of the birds' size and build. Cooper's hawks look, well, big, like a crow or pileated woodpecker in size. Sharp shin's look kind of scrawny or spindly, like a songbird someone stretched on the rack.
Of course, I could be fooling myself. There's a natural tendency among birders to default to the less common, more exotic of two options when ID is in doubt. Then every sharpie looks like a Cooper's.
