This entry is mainly addressed to David Waltz. Thanks for your interaction on this issue, David.
1) After reviewing a number of things written by Aquinas, wherein he explains in what sense the Father is greater than the Son, I have concluded that it's possible to interpret the taciturn Doctor in different ways. I understand Aquinas' application of John 14:28 to the human nature of Christ; others believe he applies the verse to both the divine and human nature of Christ, whereas yet others understand Aquinas to be saying that John 14:28 might apply to both natures.
In any event, another statement from Aquinas is found in Contra Errores Graecorum, Part One, Chapter II.:
But when Basil asserts that the Spirit is second from the Son in dignity, he appears more seriously mistaken, because he seems to posit degrees of dignity in the Trinity, whereas all three persons are equal in dignity. This statement, however, can be explained as referring, not to natural, but to personal dignity in God, just as we say that “a person is a hypostasis in virtue of a distinct property entailing dignity.” Footnote Hilary adopts this manner of speaking when he says Footnote that the Father is greater than the Son by reason of authority of origin. But by reason of oneness in substance the Son is not thereby less than the Father.
I would also suggest my own revised M.Th. thesis (my book about Tertullian), which contains a discussion of the pre-Nicenes and John 14:28.
2) Aquinas analyzes "person" language as well as cause and effect statements about God. See Part One, Chapter I of Contra Errores.
3) For Aquinas' definition of person, please see http://fosterheologicalreflections.blogspot.com/2015/04/the-trinity-doctrine-and-personhood-my.html
The Catholic Encyclopedia contains a utile article on divine personhood too. That article can be found online for the older version of the encyclopedia.
For another discussion on the western view of divine personhood, see http://fosterheologicalreflections.blogspot.com/2015/10/karl-rahner-on-trinity-qua-relations.html