What happened to Peter, James, and John's authority in the New Testament?

Les teaches that Paul made the point three times that Peter, James, and John were not above him; it was just the other way around. Les explains that they have now slipped off the scene and lost all their authority, while Paul is God's chosen vessel to take the Gospel of Grace, not just to the nation of Israel but to the whole world. Les also contrasts Paul's twenty years of ministry—one beating after another, one imprisonment after another, and constant opposition from his own countrymen—with the Twelve, who, as far as we know, did not go through such physical suffering until they were finally martyred.