An expiation changes us, taking away our sin, whereas a propitiation changes God, satisfying whatever needed to be satisfied. These are not mutually exclusive, obviously, but different atonement theories will stress one or the other. For example, in Abelard's theory, nothing is offered to God, the atonement is a demonstration of God's eternal love, whereas in Anselm's theory the atonement is an offering to God, reconciling sinful humanity to God. The former risks, among other things, falling into subjectivism and failing to take God's anger, honor, or justice seriously enough. The latter is criticized chiefly for turning the anger, honor or justice of God into a third thing beyond the Father and the Son, a necessity to which God is somehow obligated.
A further criticism of propitiation language is that it promotes views of atonement that have elements of punishment in them, thereby making its view of God morally objectionable. There is always a danger when the justice or wrath of God is separated from God's love.
But do we have to choose between expiation and propitiation? Aren't they both rightly part of a full-orbed understanding of the cross? Theologian George Hunsinger seems to think so, and in his fine book on the Eucharist, offers this useful analysis:
“God’s wrath is the form taken by God’s love when God’s love is contradicted and opposed. God’s love will not tolerate anything contrary to itself. It does not compromise with evil, or ignore evil, or call evil good. It enters into the realm of evil and destroys it. The wrath of God is propitiated when the disorder of sin is expiated. It would be an error to suppose that “propitiation” and “expiation” must be pitted against each other as though they were mutually exclusive. The wrath of God is removed (propitiation) when the sin that provokes it is abolished (expiation). Moreover, the love of God that takes the form of wrath when provoked by sin is the very same love that provides the efficacious means of expiation (vicarious sacrifice) and therefore of propitiation.” (George Hunsinger, The Eucharist and Ecumenism: Let us Keep the Feast. Cambridge: Cambridge University Press, 2008: 173-4.It also keeps us from a careless separation of God's love and wrath, and helps us realize that God's love is not some avuncular tolerance, but holy love. God doesn't tolerate our sins, but takes them away.
(Some of the above is excerpted from my When I Survey the Wondrous Cross: Reflections on the Atonement , Pickwick, 2000, Wipf and Stock, 2010)
(Picture: Matthias Grunewald's Crucifixion from the Isenheim Alterpiece)