This is a huge issue that cannot adequately be handled in a quick Q&A. Indeed, even how the question is framed needs a great deal of nuancing to understand what each side is really saying. This much I can say: The NT is clear that one cannot be saved apart from faith in Christ. And it is faith alone that saves. But the NT is also clear--as far as I have been able to determine--that one cannot simply give lip service to the gospel and live like the devil. In other words, when one truly embraces Christ as Savior, he begins a process of capturing more and more of the person's heart, mind, and will. He is the Lord objectively--regardless of what we think of him. And he becomes master of our lives as we grow in faith.
I would say that both sides of the debate have gotten some things wrong. One side says that a person must commit to Christ as Lord of his life BEFORE he can be saved. But this presupposes that a person even has the ability to change his desires apart from the work of the Holy Spirit. The other side says that all that is needed is faith in Christ and that even if the person never changes--if Christ is never made Lord of his life--then he is still saved. But that view presupposes that the Holy Spirit who is involved in saving faith has no part in sanctifying faith. In other words, both of these views have a defective view of the role of the Spirit--one in salvation, the other in sanctification. I believe that the biblical picture is that although faith alone saves, that faith will result in good works, and in a growing understanding of the Lordship of Christ. Phil. 2.12-13 are important verses along these lines.