The best use for any enemy captain during a siege is to dominate them into fighting for you immediately. This not only expands your army, but recruited captains here (in conjunction with a well-placed Wealth gem) are likely going to be of higher level than your original defenders. Recruited captains are especially useful before your defenses been have breached- they'll be the only friendly captains active outside the walls.
If you can't dominate an enemy for some reason (Too high level, iron-willed, constantly enraged or just arrow-proof and in a wild melee), then killing them for their gear is always a sound move, but consider letting one of your own captains strike the final blow. You'll still get the loot, and your captain will pick up a few extra levels on the spot, right when they're needed most.
If you're really pressed for time, then shaming them is the quickest way to get them off the field. No loot, but they immediately retreat, leaving you and your defenders free to focus on other crises.
Lastly, consider the disposition of assault leaders. Defeating the last leader in a wave immediately summons the next wave, so you might want to take that minor grace period to recruit non-leader captains before reinforcements arrive. Note that if you wait too long, the next wave arrives anyway, so don't dawdle about.