Paul felt the exceeding sinfulness of his sin. He classifies himself as the chief or first or foremost of all sinners. When you stop to look at Paul prior to his conversion you don't see a drunk, or a fornicator. You see a religious man, with strict adherence to the law. Phil. 3:4-6 enumerates some of his character (as an unregenerate man) and frankly he would be called a "good man" according to the standards of his day. (see also Acts 26:4-5) Concerning his morals, he was a straight arrow. But the Lord Jesus Christ changed his life. After realizing what he had done to the Christians, he hangs his head and remembers the persecution, injury and destruction he placed upon men and women of the faith. He then calls himself "chief" of all the sinners in the world that Christ came to die for.
I could think of other Bible characters who are worse than Paul. Who lived a morally wicked life. And yet Paul would say "I am the chief of sinners." We ought to feel the exceeding sinfulness of our sin. We must never by-pass the truth of showing lost sinners the penalty and power of sin, so that when we tell them of the Savior, it will make sense that it is the Good News. We should not compare ourselves with others, rather we ought to feel in our heart how undeserving we are of such great Salvation. God has really done a wonderful work in Salvation, Praise God that Jesus came into the world to save sinners.