Found this bird in my neighbor's front yard the other night just before dark with storm clouds rolling in. Had to shoot at ISO 1000.
In any case, the tail feather tip looks like a Cooper's, but the head was more hooded than capped. I am more inclined to have heard a call similar to the sharp-shinned than the Cooper's around the yard in recent memory.
Nice! I love the patterns of the wing feathers. Hawk could go lighter - try some selective S/H on it. As for which of the two, it's hard to say. The Sharp-shinned is normally smaller - this one looks quite bigger than the dove (?) it caught. According to my Sibley's field guide the tail on the Cooper's ends with a white band...something this one has.
To me the tail tip looks squared off, not rounded, and the head looks rather rounded. The nape has no pale-ness. All of these field marks would favor a Sharpie. It's an adult bird, so the breast feathering parttern doesn't help.
If that's a pigeon he's eating, it would indicate the size of a Cooper's Hawk. A Sharp-shinned Hawk would be about the same size as the pigeon! In addition, the feathers around the legs are more Cooper-like - a Sharp-shinned Hawk has fairly bare legs.
Stout legs, long tail, wide terminal white band on tail, hackles are not raised so the head appears rounder than square, head position doesn't reveal the nape well, outer retrices appear shorter than inner and size comparison with the Pigeon lead most likely to adult female Cooper's.
Even though the prey is a Dove. The overall characteristics of the raptor indicate Cooper's. If you have other images or can estimate the overall size of the bird that would help solidify the identification.