Even if they are unable to pick up the animal, the hawks and owls can do a lot of damage. Our neighbor's 9 pound Yorkie was almost killed in his front yard by a hawk. He survived only because he had a good layer of fat that prevented the hawk's talons from shredding vital organs. Came very close to his diaphragm.
After Jack was attacked, my father finally understood my concerns in our yard. We have hawks and owls living in our trees, so we are unable to use our yard for running around.