I've had the privilege of flying wing tip to wing tip with hawks & falcons, including peregrines, in my hang glider. One guy who was also a falconer, had a perch set up on his control bar, and his bird would rendezvous in flight.
Mostly, hawks seemed curious, and would give you a good look over. Sometimes they would object to you being in their airspace, and you would have to leave to avoid getting killed. ( full dive away was like strolling away from a greyhound ) Usually, they would give you the look over, cruise along for a while, even lead you to lift.
There was a flock of turkey vultures at Mt. Tom that would circle out front of launch, daring pilots to take off, and when you did and got to their circle, it was always a downdraft, not an updraft where they had been. They would move down the ridge as you approached, and circle just out of reach. I always thought they were laughing at us. So did everyone else.
On one special occasion, at the regional championships, the last pilot off for the day was a young lady with some fear issues on that mountain. ( mt. Utsayantha ) With no pressure to perform in the meet, a few words of mellow advice, she launched. Right after takeoff, a large hawk flew up along side, gave her the once over, and then led her to the nearest thermal. She followed this guy around the valley for 20 minutes, while we watched from launch. Eventually the hawk got bored, and started to do acrobatics, with a visible, "ok, try this!" attitude, and the pilot waved, and flew down to land after the most memorable flight of her life. She was really stoked & spooked at the same time.
Compared to a F-15, a hang glider has no speed, and no ability to climb, except by catching updrafts, but can turn in a circle nearly as tight as a large buzzard, and can generate a turn rate that even fighter jocks envy. Of course, because of their speed, a glider turning to avoid collision with a fighter just seems to sit there.
I would love to hang glide some day! Out here in Colorado I have been blessed to have been escorted by several hawks while riding and driving. Last weekend I was riding the 1125 down a hill with a gentle turn and was stretching my arms out when a hawk joined in for a few seconds, gliding just in front of me. Any road that follows a ridge line around here attracts all kinds of birds and it isn't too rare to have one flying alongside for a few seconds.
Turkey buzzards are revolting to look at up close, but they are sheer beauty in flight.