Perhaps one would say that David sinned in a more serious degree that Saul, but when confronted he had not resisted, reasoned, or fought the chastisement of God like Saul did.
Saul became murderous and mad with jealousy and perhaps bitterness when he knew that the kingship would be taken out from him.
While being hunted by Saul, David remained meek and unassuming. When David was fleeing from Absalom, Shimei threw stones at him and cursed him but this was how David responded:
2Sa 16:9 Then said Abishai the son of Zeruiah unto the king, Why should this dead dog curse my lord the king? let me go over, I pray thee, and take off his head.
2Sa 16:10 And the king said, What have I to do with you, ye sons of Zeruiah? so let him curse, because the LORD hath said unto him, Curse David. Who shall then say, Wherefore hast thou done so?
2Sa 16:11 And David said to Abishai, and to all his servants, Behold, my son, which came forth of my bowels, seeketh my life: how much more now may this Benjamite do it? let him alone, and let him curse; for the LORD hath bidden him.
2Sa 16:12 It may be that the LORD will look on mine affliction, and that the LORD will requite me good for his cursing this day. .
David also had a childlike faith, He danced without shame before the ark and fought Goliath without fear.
When we sinned against God are we repentant with a contrite spirit or do we defy the Lord's discipline, became bitter, blame others, do we reason out or complain, feeling it is not fair.
Maybe we were seriously wounded because of our sins and the scars remain to haunt us but let us rather plead with the Lord for forgiveness and healing:
Psa 51:17 The sacrifices of God are a broken spirit; a broken and contrite heart, O God, you will not despise.
Luk 5:32 I came not to call the righteous, but sinners to repentance.