"Now I would remind you, brothers, of the gospel I preached to you, which you received, in which you stand, and by which you are being saved, if you hold fast to the word I preached to you—- unless you believed in vain. For I delivered to you as of first importance…"
– 1 Corinthians 15:1-3
To be gospel-centered is to be Christ-centered. But as it pertains to the pursuit of holiness and obedience to God's commands we may opt more often for the terminology "gospel-centered," because without more qualifications, "Christ-centered obedience" can be misconstrued to imply simply taking Jesus as a moral example.
Jesus is our moral example, of course, but the power for enduring, joyful obedience comes not from trying to be like him, but in first believing that he has become like us, that he has died in our place, risen as our resurrection, ascended for our intercession, and seated to signal the finished work of our salvation.
Christ-centeredness properly qualified is truer than true. But many unbelievers have accepted (some of) Jesus' teaching as the center of their self-salvation projects. Gospel-centeredness, however, tells us in shorter fashion what of Christ to center on: namely, his finished but eternally powerful atoning work.
So we ought to take care to emphasize in our exhortations to Christ-centeredness the gospel kind of Christ-centeredness.
"[T]he simple focus of my life is to be like Christ. That is why I must let the word about Christ dwell in me richly, as Colossians 3:16 says. That is why I must gaze at the glory of Christ, 2 Corinthians 3:18, so that I can be changed into his image. That is why Christ must be fully formed in me, Galatians 4:19. That is why if I say I abide in Him I must walk the way He walked, 1 John 2. I'm to be like Christ. This is the goal of my life.
"So the goal of my life as a Christian is outside of me, it is not in me, it is outside of me, it is beyond me. I am not preoccupied with myself, I am preoccupied with becoming like Christ. And that is something that only the Holy Spirit can do as I focus on Christ. I focus on Him and the Spirit transforms me into His image."
—John MacArthur, Fleeing From Enemies