Piper and Wright differ in several key ways. The first difference is the one of scale. Wright in his preface writes "I hope, ... to sketch something which is more like an outflanking exercise than a direct challenge on all possible fronts. The latter exercise would result in hand-to-hand fighting, not only on every line in Paul." (Justification: God's Plan and Paul's Vision, Tom Wright, vii) Wright sees individual salvation as a smaller part of God's large plan. "I believe, that the salvation of human beings, though of course extremely important for those humans, is part of a larger purpose." (Justification, 8) While Piper agrees with Wright's big picture; "One of Wright's passions is to help us see more clearly the historical sweep and global scope of God's purposes in the gospel. This accounts for some of his reactions to the individualism and pietism that mark some preaching of the gospel," (The Future of Justification, John Piper, 81) he also wants to show how Justification isn't just a big picture thing but something clearly applicable to individuals. The scale of what Wright is proposing isn't a radically new thing, Reformed theology has emphasised a grand covenantal narrative for along time.
Douglas Wilson writes:
This is great stuff, but it is hardly Columbus planting the flag on a virgin continent. Find me one word in that summary that would not bring forth a chorus of amens from B.B. Warfield, Jonathan Edwards, or any Reformed stalwart between the years, say, 1550 and 1900. ... Wright really needs to get out more, and stop acting like he has discovered things that many Christians have known and taught over the course of generations.
Interestingly Kevin DeYoung says almost the same thing:
Has the whole Western tradition missed this story? Really, we are just now seeing it by virtue of the Sanders revolution? Did Ridderbos miss this? Or Vos? Or Edwards with his massive history of redemption? ... Piper, Carson, Westerholm, Luther, Hodge et. al don’t need me to come to their defense. But does Wright think they do not also believe and teach the grand meta-narrative of Scripture? They may want to go back to Adam and put Abraham and Israel in the broader context of fall and redemption, but surely they see the same God-through-Israel-for-the-world narrative without embracing the New Perspective.
Piper wants to talk about the nitty gritty of justification in a person's life while Wright wants to make some grand out flanking maneuver to avoid the smaller focus. The problem is that it's already part of Reformed theology to think of salvation as grand narrative through the Old and New Testaments. However just because our society has over-emphasised individualism doesn't mean that the large scale narrative of salvation doesn't have an individual application.