There is some major doctrinal discontinuity between these two notable theologians, especially concerning the identity of the “one God” of the Christian faith.
As has been previously noted on this blog, Augustine was a strong early proponent of the idea that the one God of the Christian faith is the Trinity. We see this idea thus expressed by his own pen:
“That one God, therefore, the Father and the Son and the Holy Spirit, who will not appear, except for joy which cannot be taken away from the just…” (On the Trinity, Book 1, Ch. 13)
“…neither here does it appear plainly whether it was any person of the Trinity that appeared to Abraham, or God Himself the Trinity, of which one God it is said, You shall fear the Lord your God, and Him only shall you serve.” (Book 2, Ch. 10)
“O Lord the one God, God the Trinity, whatever I have said in these books that is of Yours, may they acknowledge who are Yours; if anything of my own, may it be pardoned both by You and by those who are Yours. Amen.” (Book 15, Ch. 28)
In contrast, Irenaeus of Lyons, on the other hand, can be noted to be equally emphatic in proclaiming that the one God of the Christian faith is the person of the Father in particular:
“And others of them, with great craftiness, adapted such parts of Scripture to their own figments, lead away captive from the truth those who do not retain a stedfast faith in one God, the Father Almighty, and in one Lord Jesus Christ, the Son of God.” (Against Heresies, Book I. Chapter III. 6.)
“The Church, though dispersed through out the whole world, even to the ends of the earth, has received from the apostles and their disciples this faith: [She believes] in one God, the Father Almighty, Maker of heaven, and earth, and the sea, and all things that are in them; and in one Christ Jesus, the Son of God, who became incarnate for our salvation; and in the Holy Spirit, who proclaimed through the prophets the dispensations of God” (Against Heresies, Book I. Chapter X. 1.)
“These have all declared to us that there is one God, Creator of heaven and earth, announced by the law and the prophets; and one Christ the Son of God. If any one do not agree to these truths, he despises the companions of the Lord; nay more, he despises Christ Himself the Lord; yea, he despises the Father also, and stands self-condemned, resisting and opposing his own salvation, as is the case with all heretics.” (Against Heresies, Book III. Chapter I. 2.)
“And therefore it is right first of all to believe that there is One God, the Father, who made and fashioned all things, and made what was not that it should be, and who, containing all things, alone is uncontained.” (The Demonstration of the Apostolic Preaching)
While both theologians appeal to scripture in support of their position, it is clear which of these viewpoints actually represents the biblical position:
“There is one body and one Spirit, just as also you were called in one hope of your calling; one Lord, one faith, one baptism, one God and Father of all who is over all and through all and in all.” Ephesians 4:4-5 NAS
“This is eternal life, that they may know You, the only true God, and Jesus Christ whom You have sent.” John 17:3 NAS
“…yet for us there is but one God, the Father, from whom are all things and we exist for Him; and one Lord, Jesus Christ, by whom are all things, and we exist through Him.” 1 Corinthians 8:6 NAS
It is also noteworthy, that although Augustine lived after the Nicene Council and knew of its Creed, it is Irenaeus, who lived prior to the Council, who is doctrinally in agreement with its decision, not Augustine:
“We believe in one God, the Father Almighty…” (First words of the Nicene Creed)
Another point of contrast, already noticeable above, is that Irenaeus is in agreement with and appeals to the church’s tradition as further testifying to the truth of what he says. He speaks not of his own novel opinions, but declares that the whole church believes what he is saying pertaining to the one God of the Christian faith being the person of the Father in particular. Irenaeus not only goes to great lengths to show what he is saying from the scriptures, but also includes the historical testimony of prior church fathers, and the contemporary church of his day.
Augustine, on the other hand, appeals to scripture to as supportive of what he says (although ultimately failing to provide any proof on this particular point of doctrine), but does not rely heavily on historical testimony or the church’s tradition on this point of doctrine. This is of course because most prior theologians did not hold his view, but rather that of Irenaeus.
Augustine makes some general appeals to those who came before him, but does not even seem to be aware that he is disregarding the doctrine of most orthodox theologians prior to him. It may be conjectured that this was due to his receiving his doctrine from his immediate predecessor, Ambrose, and other early semi-modalists in Rome and the west. If this is so, then we cannot fairly view Augustine as an innovator on this point, but as faithfully following a new school of thought that can be traced back to a few years before his conversion, which he received from his teachers. Thus he can appeal to those who came before him, while ultimately disagreeing with most of the ancient church.
Historically western theology since the time of Augustine has generally taken his position as fact without question, largely ignoring the testimony of the Irenaeus, and of scripture. Perhaps as Irenaeus’s position is better understood by western scholars we will see a return to the classical trinitarianism taught not only by him, but by many orthodox church fathers in the nicene and ante-nicene eras. Such a revival of interest in classical trinitarianism and Irenaeus’s articulations of that can be seen in the contemporary Eastern Orthodox church, a fact which may appear a bit ironic when we consider that he was a western church father (Lyons being in modern day France).
For more quotes from Irenaeus on the subject, as well as from other fathers, see here: https://nicenefaith.wordpress.com/2017/03/08/i-believe-in-one-god-the-father-almighty/.