Objection 1. It would seem that the Son is not equal to the Father in greatness. For He Himself said (John 14:28): "The Father is greater than I"; and the Apostle says (1 Corinthians 15:28): "The Son Himself shall be subject to Him that put all things under Him."
Objection 2. Further, paternity is part of the Father's dignity. But paternity does not belong to the Son. Therefore the Son does not possess all the Father's dignity; and so He is not equal in greatness to the Father.
Objection 3. Further, wherever there exist a whole and a part, many parts are more than one only, or than fewer parts; as three men are more than two, or than one. But in God a universal whole exists, and a part; for under relation or notion, several notions are included. Therefore, since in the Father there are three notions, while in the Son there are only two, the Son is evidently not equal to the Father.
On the contrary, It is said (Philippians 2:6): "He thought it not robbery to be equal with God."
I answer that, The Son is necessarily equal to the Father in greatness. For the greatness of God is nothing but the perfection of His nature. Now it belongs to the very nature of paternity and filiation that the Son by generation should attain to the possession of the perfection of the nature which is in the Father, in the same way as it is in the Father Himself. But since in men generation is a certain kind of transmutation of one proceeding from potentiality to act, it follows that a man is not equal at first to the father who begets him, but attains to equality by due growth, unless owing to a defect in the principle of generation it should happen otherwise. From what precedes (27, 2; 33, 2,3), it is evident that in God there exist real true paternity and filiation. Nor can we say that the power of generation in the Father was defective, nor that the Son of God arrived at perfection in a successive manner and by change. Therefore we must say that the Son was eternally equal to the Father in greatness. Hence, Hilary says (De Synod. Can. 27): "Remove bodily weakness, remove the beginning of conception, remove pain and all human shortcomings, then every son, by reason of his natural nativity, is the father's equal, because he has a like nature."
Reply to Objection 1. These words are to be understood of Christ's human nature, wherein He is less than the Father, and subject to Him; but in His divine nature He is equal to the Father. This is expressed by Athanasius, "Equal to the Father in His Godhead; less than the Father in humanity": and by Hilary (De Trin. ix): "By the fact of giving, the Father is greater; but He is not less to Whom the same being is given"; and (De Synod.): "The Son subjects Himself by His inborn piety"--that is, by His recognition of paternal authority; whereas "creatures are subject by their created weakness."
Reply to Objection 2. Equality is measured by greatness. In God greatness signifies the perfection of nature, as above explained (1, ad 1), and belongs to the essence. Thus equality and likeness in God have reference to the essence; nor can there be inequality or dissimilitude arising from the distinction of the relations. Wherefore Augustine says (Contra Maxim. iii, 13), "The question of origin is, Who is from whom? but the question of equality is, Of what kind, or how great, is he?" Therefore, paternity is the Father's dignity, as also the Father's essence: since dignity is something absolute, and pertains to the essence. As, therefore, the same essence, which in the Father is paternity, in the Son is filiation, so the same dignity which, in the Father is paternity, in the Son is filiation. It is thus true to say that the Son possesses whatever dignity the Father has; but we cannot argue--"the Father has paternity, therefore the Son has paternity," for there is a transition from substance to relation. For the Father and the Son have the same essence and dignity, which exist in the Father by the relation of giver, and in the Son by relation of receiver.
Reply to Objection 3. In God relation is not a universal whole, although it is predicated of each of the relations; because all the relations are one in essence and being, which is irreconcilable with the idea of universal, the parts of which are distinguished in being. Persons likewise is not a universal term in God as we have seen above (Question 30, Article 4). Wherefore all the relations together are not greater than only one; nor are all the persons something greater than only one; because the whole perfection of the divine nature exists in each person.
Source: Summa Theologica (New Advent)