When we talk about equality, we are speaking in terms of measurement. We must specify the units by which we are affirming equality if we are to make good sense out of what we mean by the term. All human beings are equal in the eyes of the law; we have equal civil rights. All Catholics are equally blessed by the sacraments: we are baptized with the same baptism, absolved from our sins by the same Savior, filled with the same Holy Spirit in Confirmation, and given Jesus Himself, whole and entire, in Communion. Humans are not equal in age, weight, hair distribution, and many other measurable or observable dimensions.
One pound of feathers is equal in weight to one pound of gold. Feathers and gold are not of equal worth for making pillows or making rings or for making a killing in the commodities market.
The Father, Son, and Spirit are equal in every perfection which belongs to the Godhead, because the three Persons are "one in being" (homoousios) with each other: glory, majesty, power, beauty, truth, eternity, knowledge, freedom, presence. The difference in the Persons is one of relationship--they do not have the same (identical) relationship with each other. The Son is from the Father; the Spirit is from the Father and the Son (filioque clause); the Father alone has no origin--He is the only person in the whole universe of personal beings who has no father. Every other person (divine, angelic, human, extra-terrestrial) is from the Father.
The Trinity is our model of the union of equal persons who are not identical to each other. This model is essential for grasping the nature of marriage and the hierarchical structure of the Church.