I still have trouble at times telling the difference between a Sharp-shinned Hawk and a Cooper's Hawk. I've read a number of resources to help differentiate them, and just when I think I have it down, I see one that I just can't quite identify with certainty.
The problem is you can't just use one field mark to tell the difference. Cooper's Hawks are bigger...sometimes. Sharpie's tails look squared off...sometimes. And then there's the comparative field marks like the Cooper's head is larger or the sharpie legs are thinner. Yeah, if they were sitting side-by-side, that would be easy! And I find the in-flight characteristics like the Cooper's slower wing beats, or that the sharpie's small head doesn't extend past the wings even harder to pick out.
So I like when one of them flies up, nice and close, sits for a just a little while, and shows a number of field marks nice and clearly with little room for interpretation.
Like this guy (or gal). Rusty barring on chest, slaty back, red eye tells me adult bird, either species. That's the easy part. Smaller size...thinkin' sharpie. Nice squared off tail...another point for a sharpie. Skinny little legs...sharpie. More subjective (to my eyes) is the broader chest and narrower bottom of the sharpie.
Here's two good sources:
Tricky Bird IDs on the Cornell Lab Project FeederWatch site and Kaufman Field Guide to Advanced Birding