Theological Tuesday--Trinity Questions

For about two weeks, the Christian Concepts were focused entirely on the Trinity. In thinking more about this doctrine, I have some questions that I think would be interesting to discuss. For instance, how are the three Persons of the Trinity different from each other? Or are they different, other than in the sense that they are three? What I mean is something like this. If God the Father is omnipotent, then God the Son can’t also be omnipotent, can He? If you have two omnipotences, that would seem to be a problem. This raises the question of whether each of the three (Father, Son, and Holy Spirit) are each individually perfect/complete/sufficient/omni-whatever, or are they only these things when taken altogether as a unity? Also, a question came up in a personal discussion recently of whether the Father is superior to the Son (and where does the Holy Spirit fit in here, anyhow) or whether they are equal in authority or even equal in their “share” of the Godhead? I will say in advance that I’m not sure of my own answers to these questions, so I thought it might be worth discussing.