Why was David forgiven, but Saul not?

A brief comparison with 1 Samuel 15 is quite illuminating. Besides the reoccurrence of the expression of God’s change of mind concerning the punishment (נחם [nḥm]; cf. 1 Sam 15:29, 2 Sam 24:16), in both accounts we find reference to the sin of a king. In both instances, God sends a prophet in the morning to draw attention to the monarch’s transgression (cf. 1 Sam 15:12, 2 Sam 24:11). This is followed on both occasions by a double royal confession of guilt (cf. 1 Sam 15:24, 30; 2 Sam 24:10, 17). Initially, however, Saul sought to justify his failure by blaming the people (1 Sam 15:14, 21), while David fully acknowledges his guilt and is eventually ready to take upon himself all the punishment (2 Sam 24:17). Saul is not even ready to accept his own judgment (1 Sam 15:24–25). In fact, Saul does not change much during the conflict with Samuel, while David acknowledges the divine word communicated through the prophet and thus repented genuinely. Authentic repentance of sin averts the wrath of God and often leads to the reestablishment of the divine-human relationship. By praying that Yhwh would redirect the punishment onto himself, David appears to earn the right to pray for pardon for the people. David’s prayer was heard.—Standing in the Breach, page 244