How do the Father and Son differ if they have the same particular essence?

My question assumes ousia in Christian orthodoxy means a particular (not universal) essence or form, and not a concrete instantiation (hypostasis). If the Father and Son have the same ousia, where are the properties that distinguish them? Does the hypostasis have additional distinguishing properties? If so, are these properties necessary or contingent? If necessary, how are they definitionally excluded from the ousia?