Coopers and red tails are pretty distinctly different. Size is the first marker as red tails are significantly larger than coopers hawks. Also, coopers have very distinctive barred breasts and banded tails. You can also differentiate them through their wing profile; red tails are buteos and have a broad wing profile that is largely straight while coopers are accipitors and their wings are much more angular so that they can more deftly maneuver through wooded areas.
Snagging pigeons off of ledges would point me toward Peregrine falcon, but it’s far from definitive.