The eagle was/is such a common symbol of government that Ben Franklin wanted the national bird to the the turkey. A species far more intertwined with colonial history. However, turkey's go into sandwiches and aren't major birds of prey, so understandably those settling on national iconography tilted towards eagles.
You know, I've walked by that building countless times, and besides its massive size it's never really caught my eye. Guess I'll have to pay more attention next time I go by there.