It would be helpful, I think, to get a full definition and description of the Catholic view and the Orthodox view.
In Rom. 6 we get a picture that we are slaves to sin, which is death. We are able to overcome this bondage by uniting ourselves to Christ in baptism. Because of this we are freed from bondage and death, “For if we have been planted together in the likeness of His death, certainly also we shall be of the resurrection….” (Rom. 6:5)
There are two way of redeeming something, either by buying it back, or by defeating the one who holds it. Rom. 6:6 indicates which of these Christ accomplished on the cross: “…knowing this, that our old man was crucified with Him, that the body of sin might be rendered inactive….” We also see this same concept in the Old Testament examples of redemption, most obviously in how God redeemed Israel Egypt. He didn’t come in and buy them back from Pharaoh, God forcefully took them from him. They were freed from bondage by force.
It is this understanding that we have reflected in our Paschal hymns, that Christ defeated death by death and on those in the tombs bestowed life. It was a defeat of Satan who held us bound to death with our sins. Christ invades our world and takes back what is His. St. Irenaeus shows that this was the view of the early Church:
“For if man, who had been created by God that he might live, after losing life, through being injured by the serpent that had corrupted him, should not any more return to life, but should be utterly [and for ever] abandoned to death, God would [in that case] have been conquered, and the wickedness of the serpent would have prevailed over the will of God. But inasmuch as God is invincible and long-suffering, He did indeed show Himself to be long-suffering in the matter of the correction of man and the probation of all, as I have already observed; and by means of the second man did He bind the strong man, and spoiled his goods, and abolished death, vivifying that man who had been in a state of death. For at the first Adam became a vessel in his (Satan’s) possession, whom he did also hold under his power, that is, by bringing sin on him iniquitously, and under color of immortality entailing death upon him. For, while promising that they should be as gods, which was in no way possible for him to be, he wrought death in them: wherefore he who had led man captive, was justly captured in his turn by God; but man, who had been led captive, was loosed from the bonds of condemnation (
Against the Heresies,” Book 3, Chp. 23).”
In this understanding, Christ defeats death in us with His life, uniting us to Him, and overcoming Satan and death with His Life.
Christ is considered the reality which the Old Testament sacrifices point to. Christ did take our place in death and defeat it, and thus He did substitute Himself in our place who were to die. The whole sacrificial nature of Christ’s death is clearly portrayed in Hebrews 9 and 10: “But He, having offered one sacrifice for sins in perpetuity, ‘sat down on the right of God….’” (Heb. 10:12). St. Peter also indicates this, “knowing that ye were not ransomed with corruptible things…but with the precious blood of Christ, as of a lamb without blemish and without spot….” (1 Pet 1:18-19)
From the liturgical material of the Church, we understand that the one Old Testament sacrifice which points to the nature of Christ’s purpose on the cross is the Passover Lamb. It was this sacrifice, the central sacrifice by which the Israelites were redeemed from Egypt, that illustrates how Christ with His sacrifice redeems us from the bondage of Satan and death. Death passes over those who have eaten Him and as St. John Chrysostom so graphically says, smeared His blood on the doorpost of our mouth. The liturgical material on Pascha speaks frequently of Christ being the “new Pascha”, in that we have been brought from death to life.
To that end, all the sacrifices in the OT point even if they were for other purposes. They also all were icons pointing to Christ’s sacrifice on the cross, where His body was broken and His blood was poured out that as St. John says in John 6, we might eat His flesh and drink His blood. In His flesh and blood is true life. To eat, He must be sacrificed and Satan is defeated.