These are two tough birds to separate. From what I have read, here are some comparisons that can help.
1. Size. Cooper's are abut the size of a crow while a sharp-shinned is about the size of a jay. But there is overlap between a large female sharp-shinned and a small male Cooper's. In this picture, we have no real guide to size.
2. Shape of the head. Cooper's tend to have a blocky head (often appearing a bit oversized) while a sharp-shinned has a more typical rounded head (often appearing slightly undersized). This picture shows a more rounded, smallish head.
3. Dark cap or not. Cooper's tend to have a lighter-colored nape (back of the neck) and the dark coloration does not extend below the eyes. It looks like they are wearing a dark cap. In a sharp-shinned hawk, the nape is darker and the dark coloration extends below the eyes. Without seeing a posterior view, I would give the edge to sharp-shinned.
4. Shape of the tail. In a Cooper's hawk, the tip of the tail is often rounded, while the tip of the tail of a sharp-shinned hawk is flat. Cooper's hawks also appear to have longer tails and a broader white tip. Assuming that the tail feathers here are not worn down, I would give the nod to sharp-shinned hawk.
Overall, I would call this a sharp-shinned hawk.
Steve