I like to think that the choice of the eagle by Gaius Marius had more to do than just the association with Jupiter. When one considers the Roman art of war in comparison to other nations of the time, you get an impression of a finer form of attack. The Gauls and Germans rely on brute strength. The Greeks and Cartheginians their massive phalanxes, the Numidians their horses.
The Roman relys on choosing his battles carefully because he is usually outnumbered. The Roman fights not with a huge pike nor a two-handed sword, but a short, sharp sword, used to make precision stabs rather than gaping wounds or the hope of any wound in a forest of pike.
The Roman fights and kills as the eagle does, not like the bull, the horse or the boar.