If you have hawks and crows in your area, you know that crows know exactly how to handle hawks. They attack from above, diving down on the hawk because they know the hawk can't suddenly fly upward to grab them. I have, however, seen a hawk flip onto its back to try to catch an attacker coming from above, but this is pretty rare. My strategy is #1 stay away from hawks and eagles when possible, but if I ever see one diving on my MP, I hope I'd have the presence of mind to go UP Up and AWAY at the same time.
Most hawks that you see circling in the sky in N. America are Red-Tailed hawks. They are for the most part ground feeders,catching snakes, squirrels and rabbits. I've never seen one catch anything in the air. They're big and not terribly agile flyers.
Hawks that hunt other birds are usually falcons, and you rarely see them circling. They typically hunt from a perch. They fly straight and fast, catching prey from behind or while on the ground. They don't soar, but flap, glide, flap, glide for the most part.
As to the territoriality of red-tails, I spent one spring observing three nests within a half mile of each other and never observed any territorial disputes among the nesting pairs. Red tails drift and hunt over huge expanses. One that's directly overhead may be a mile away a few minutes later. I'm guessing that if they dive on a drone, they think it's prey. And their prey flies straight and fast. They know how to compensate for that movement.
Golden Eagles and Bald Eagles also mainly eat things they catch at ground or water level, but will hunt waterfowl also. Flying waterfowl go straight and fast, so trying to escape by flying horizontally way from a hunting eagle seems like a BAD idea. If the attacker is coming from a distance, going up may not save you, but it will no doubt surprise the eagle because its normal prey can't do that.
Well, I'm just thinking out loud here, based on years of observing hawks and eagles in action. Hope this helps a little. UP UP AND AWAY!