The choice matters because it decides whether the atonement has to deal with anything in God.
If the word means expiation, then what the cross removes is sin, and the models that require a divine disposition to be changed lose their strongest single text. Penal substitution can still be argued, but not from this word. Christus Victor, recapitulation and moral influence all sit comfortably with expiation, since none of them needs God to be turned from anger.
If the word means propitiation, then wrath is in the account and has to be dealt with rather than explained away, and the models built around penalty and satisfaction have their central vocabulary underwritten. Defenders of that reading are careful to say that divine wrath is not temper or malice but the settled opposition of God to what destroys people, and that a God who is not opposed to such things is not good. Their critics answer that the careful definition is not what the word does in practice, and that the pulpit version is a God who has to be calmed.
Two further points keep the question from being tidy.
The first is that the translation history reads as a record of doctrinal alignment. Propitiation in the Authorised Version, expiation in the Revised Standard Version, and a neutral phrase in several later ones. Readers noticed each time, and the objections raised on each occasion were doctrinal rather than lexical.
The second is that a number of theologians hold that the disjunction is false, and that in the biblical setting the same act does both, since it is God who provides the means by which sin is dealt with. On that reading the objection to propitiation, that it makes God the passive recipient of an offering someone else brings, is answered by the observation that in the text God is the subject of the sentence and not its object. Whether this resolves the question or restates it is itself argued.