I am strongly leaning the other way. I am 99% sure it is a Sharp shinned.
In profile a mature Coopers has a raised, straight ridge line or brow above the eye. It tends to give it a sinister look. The Sharp shin has a gently rounded head, making it sweeter or cute looking. That bird has a round head.
Coopers tend to be between 15-20" tip of beak to tip of tail. The smaller birds tend to be males.
Sharp shins are 11-15" from tip of beak to tip of tail. Do not include the legs. A Coopers sits proudly on longer legs. I have rarely seen one hunch over. That bird is not 15-20" long in my mind.
Coopers do not typically bother with small songbirds like sparrows or finches. Those are too small for them to catch! Sharp shins are much more maneuverable and can catch sparrows much more easily. Coopers love to catch Cardinals, Mourning Doves and Ring neck Doves. Being bigger birds, those make a much better meal.
Plus I am basing my opinion on familiarity. I have seen somewhere around 10,000 Sharp shins in my bird watching life and perhaps 700 Coopers. Both are bird eating Accipiters, but the Coopers with its pronounced brow line and flatter head, reminds me of 'Frankenstein'.
A Coopers has much longer legs and longer tail but we can't see those here.
But when you are fortunate enough to see a Coopers, it is a big bird. Shockingly so compared to a Sharp shin. But all of that comes with experience. It takes hundreds and hundreds of sightings to get comfortable with identification of these. That bird sitting on the arm of that chair is not shockingly big.
And as I often tell my bird watching beginners in my classes, more mistakes are made over estimating the size of a bird. "They just absolutely refuse to sit next to a ruler"!!!
