Difference between Saul and David

Their sins
Saul did not kill all that God asked him to:
Then Saul slaughtered the Amalekites from Havilah all the way to Shur, east of Egypt. He captured Agag, the Amalekite king, but completely destroyed everyone else. Saul and his men spared Agag’s life and kept the best of the sheep and goats, the cattle, the fat calves, and the lambs — everything, in fact, that appealed to them. They destroyed only what was worthless or of poor quality. (1 Samuel 15:7-9 NLT)

David commited adultery and murder:
Late one afternoon, after his midday rest, David got out of bed and was walking on the roof of the palace. As he looked out over the city, he noticed a woman of unusual beauty taking a bath. He sent someone to find out who she was, and he was told, "She is Bathsheba, the daughter of Eliam and the wife of Uriah the Hittite." Then David sent messengers to get her; and when she came to the palace, he slept with her. She had just completed the purification rites after having her menstrual period. Then she returned home. Later, when Bathsheba discovered that she was pregnant, she sent David a message, saying, "I'm pregnant." (2 Samuel 11:2-5 NLT)
Some of the king's men were killed, including Uriah the Hittite. (2 Samuel 11:24 NLT)

Their reaction when confronted by the prophets:
Saul was interested in looking good before the people.
Then Saul pleaded again, "I know I have sinned. But please, at least honor me before the elders of my people and before Israel by coming back with me so that I may worship the LORD your God." (1 Samuel 15:30 NLT)

David publicly confessed his sins:
Then David confessed to Nathan, "I have sinned against the LORD." (2 Samuel 12:13 NLT)

God's response:
God rejected Saul but built a house for David.