Are the tips of the eagle's wings wide spread, or drooped to the sides of the eagle? There are several good books on WBTS artifacts which deal with the different types of buttons. As riflepit said, the Eagle button was quite common and there were two different basic type one was primarily used by the Union, while the other was primarily used by the Confederates.

However, this does not mean that the Union eagle button were not used on Confederate uniforms. It was not uncommon for buttons manufactured in Philadelphia to be used on southern Uniforms. Especially early in the War.