I, personally, like to have aseries of asymmetries across all the grounds (foreground, middleground, background) that all come together to form one well balanced image that is easy to look at. If the foreground is the plane, for example, I try to not have the plane centered in the shot, because to me, beauty in photography does not come from symmetry in your grounds, but asymmetries that equal out.

Plus, having asymmetries in a picture allows you to have less of the foreground, middleground or background being blocked in by each other.

Symmetry is important, but it is NOT an axiom.