Great picture!  Raptors are so hard to identify.  I have books and books on identifying hawks.  I rarely get to see them sitting still--it is usually just a two-second miscellaneous brown blur I see.
 
I think the bird you pictured is an adult--juveniles have a barred chest.  The adults have the orange chest and belly.
 
 
I have a resident pair of Red Shouldered  hawks nesting within 100 or 150 feet of my house.  They defend their territory from other hawks, and with their distinctive call, I know if all is not well in the area.
I had what I think was a Red Shouldered giving chase to one of my smaller macaws (500 grams) this year.  It was either a Red Shouldered or a Coopers.  I was impressed at how easily the bird stuck with my bird as my bird dodged in and out of the trees--just 18 inches behind and just off my bird's hip no matter which way my bird zigged or zagged.  I don't think the hawk was actually intending to catch my bird; it seemed to be just an instinctual  chase or a curious bird.  When my macaws first moved in, we had a lot of curious vultures that kept flying over to see the big brightly colored macaws.  They were a real nuisance for the first year I flew here because they would come from miles around to have a really close look.  My macaws freaked and the big Scarlet would fly off over the horizon for a few hours.  She doesn't seem bothered much by the vultures now, but early on she just panicked.
 
I've seen one bird kill a dove this year--don't know what kind of hawk, just a brown blur and an explosion of feathers from inside the tree.  I would suspect a Coopers, but I have yet to see one or hear one.  I hope my Red Shouldered pair keep the Coopers out of my area.  A big female Coopers is a formidable adversary for my macaws--ambush predators, incredibly fast and agile but like a Cheetah, not good for anything other than a sprint.  Out in the open, my macaws are safe, but in the trees on my property?  Not so sure.   Hopefully, my falcon-expert friend is right that no hawk is going to be stupid enough to tangle with my macaw.