A Cooper's Hawk is a bird frequently misidentified as a Peregrine falcon.
Here is a side by side of a (male) Coopers Hawk (photo taken in Avon, IN) and of Kinney, the male peregrine downtown (photo taken by Scott Sefton, photographer - SRS-Photo ).

The peregrine head is "hooded", the Cooper's is "crowned".
While you can't see Kinney's tail, the Cooper's is quite a bit longer than a peregrine's and the bars are more distinct on the Cooper's.
The peregrine has a light "bib" (generally the male's is lighter and bigger than the female's), the Cooper's color bars go up to the face.
The adult Peregrine and the Cooper's both have the horizontal looking coloring in the front, but the Cooper's is lighter and in general broader markings.
While you can't see it on the Cooper's, their legs do not have the "leggings" the Peregrine's do.
Also, both Kinney and KathyQ are banded. Cooper's Hawks, not being endangered are never banded. THAT is a huge giveaway if all else fails.