How I deal with captured rebels depends on my situation in the overall campaign, but I always give my king the choice of thumbs up or thumbs down. If my general regularly executes prisoners, there is a morale penalty so I only use that option when I have captured an important general who fights for another faction.

If there are no real external threats at the moment, and I dont expect any real threats in the next 20-30 turns, I execute them all so my king gets the no justice vice (greatly reduced province loyalty) as beating down lots of rebellions increases the command rating of my generals and royal heirs.

If I am taking lots of territory off my enemies in a major war, my king releases all rebels, including the leaders, to get the most merciful virtue, so I have less problems with province loyalty as I rush troops off to the front.