Well, that depends. Is grappling and elbow strikes allowed?
After having watched some videos just now of eagles fighting in the wild, I am certain that most concerning is the claw!
I'm also happy to report that I found more info re: the bald eagle. It appears he is an opportunist and a thief, despite his noble appearance. Instead of hunting for his own food, he prefers to muscle out other more hardworking birds from their meals. To me, this means -1 point in the fight with the Polish eagle. Also, I found out that both birds are very stupid, especially when compared to crows or macaws. The bald eagle, for example, is not smart enough to walk into shelter when it's raining, and instead just sits there getting soaked. Again, -1 point for the Bald Eagle.