As symbols they are more than a representation of the bird itself. They often symbolize a specific quality like love, peace, strength or bravery. The eagle was often used as a military decoration. Large gold eagles crowned cannons, and small paintings graced Civil War drums. Most of us think of the eagle as a symbol of courage, and having strength and hope.
Roosters are a common bird seen on barns as well as weathervanes.
Originally the reason was a religious one. It was chosen as a symbol of the denial of Christ. Peter denied Christ before the cock crowed twice. Beginning in the Middle Ages a cock was placed on a church spire to remind the people not to do likewise. The rooster became a symbol of watchfulness.