Wow, I had no idea a bald eagle was that big. I think the eagle could possibly have a hard time catching the cat from such a close distance. That sounds absurd, but cats are insanely fast and eagles usually kill from above. Still, I'm surprised the cats stuck around.
I think that they'd BOTH die if they got in a fight... the cat before the eagle.
Cat claws have huge amounts of bacteria... even a small wound can become infected enough to kill a bird. (Speaking from experience with parrots...)
"There is no greater wonder than the way the face and character of a woman fit so perfectly in a man's mind, and stay there, and he could never tell you why. It just seems it was the thing he most wanted." Robert Louis Stevenson