The Cooper's Hawk looks very similar to the Sharp-shinned Hawk.
Their size is not always indicative because a female Sharp-shinned Hawk can be as large as a male Cooper's Hawk.
However, the Cooper's Hawk's tail is usually rounded at the tip (square with Sharp-shinned Hawk) and the middle tail feathers are usually the longest (Sharp-shinned Hawk's outer tail feathers are usually the longest) .
In addition, the legs of the Cooper's Hawk are thicker and usually Cooper's Hawk has a more "fierce" facial expression.

1st, 2nd & 3rd photo: Bosque Del Apache National Wildlife Reserve, San Antonio, New Mexico, USA, 13 January 2019
4th & 5th photo: Rio Grande Nature Center State Park, Albuquerque, New Mexico, USA, 16 January 2019