In a fight between a bald eagle and a red-tailed hawk, the bald eagle would likely win. Bald eagles are more aggressive and have a more powerful attack than red-tailed hawks. Red-tailed hawks are more agile and can fly faster than bald eagles, but they would not be able to match the bald eagle's strength and power in a fight.
Bald eagles typically do not go out of their way to hunt red-tailed hawks, but will kill and eat them if the opportunity arises. Red-tailed hawks are generally larger than most of the other birds that bald eagles prey on, and therefore it may take more effort for the eagle to kill the hawk than the benefit received.