All the tactics here are good but I have to back Saul, if you manage to destroy the BGs before they rout, the King is killed.

Surround with a high tier spears unit, then chase him down with fast cavalry. If you have one unit of cavalry right outside where the fighting is going on, and a stronger (albeit slower) unit farther away where you expect him to run, you can almost always intercept him with a high success rate.

IMO, killing any faction leader is always for the better. Your general usually gets a stat boost AND you get the satisfaction of killing the scumbag. I usually kill prisoners after a battle to increase my general's dread (which I think is the most useful stat after loyalty) so the enemy can shit their pants while fighting him.