One should remember, that knights really often were wearing perfectly open helmets from IX to XV century EDIT: XVI century too, I guess. Maciejowski Bible shows us a lot of knight in open normans, or even mail hoods.
In earlier ages there weren't any closed options really. And from about half of the XIV century, neat bascinets with visors begin to appear, which allow you to "switch" between open and fully protecting helmet with hand motion.
Later closed helmets are usually well adjusted (particullary armets) and one have nice static visor to look trough.
Barrel helmets would be probably worst, since they're a bit "loose" on the head, but some better adjusted examples weren't probably so bad either.
If someone's laying on the ground, dropped violently from horse, and you stand above him with something "convincing", he would better surrender, armor or not.
Or your man at arms just grab him, tie him and take him. People are always wonder about strikes etc, forgetting that armor doesn't help THAT much, when few people want to just drop you and immobilize you.
I would certainly assume that taking prisoner was NOT happening in the middle of biggest bashing.