The contrasts between Saul and David appear throughout 1 Samuel. Here are just a few of them to consider along the way.

	Saul	David
Tribe	Benjamin	Judah
Patronym	Son of Kish	Son of Jesse
Description	…a handsome young man. There was not a man among the people of Israel more handsome than he. From his shoulders upward he was taller than any of the people.	Now he was ruddy and had beautiful eyes and was handsome.
Herding	Lost Donkeys	Contented Sheep
Found	Wandering through Ephraim, Benjamin and Zuph	In his father’s fields, tending the flock
The Feasts	Public in Mizpah	Public in Bethlehem, but David does not attend
Relationship to Samuel	YHWH sends him to Samuel	Samuel goes to him
Anointed	Alone, outside of town	In front of his family, in town
After his anointing	The Spirit comes upon him	He plays for Saul, because the Spirit has left him

Of course, I’m only one reader but it does seem rather strange that this many things appear in both narratives. It only makes sense that it is an intentional device meant to contrast the two kings and show the clear superiority of David.