It would be a complete and utter draw. The Dead Army were used as a scare device by Aragorn, they were 'shadows barely visible to the eye,' and could not do any physical harm to any physical being on Middle-earth. They could of course scare people, as they did with the corsairs, but nothing else. A 'shadow' or a 'spirit' is something that is intangible, and cannot bring physical harm to anyone or anything, they are more or less just there. As is the case with Sauron when the Ring is destroyed:
Quote:
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...if the One Ring wwas actually unmade, annihilated, then its power would be dissolved, Sauron's own being would be diminished to a vanishing point, and he would be reduced to a shadow, a mere memory of malicious will.~Letter to Milton Waldman
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Sauron would be reduced to a 'vanishing' point, but the Dead Army curse was for their spirit to never 'rest' until their oath to Gondor was fulfilled. And again, being called 'shadows' would mean they could not have done any physical harm.
Now the Witch-King was invisible, but unlike the King of the Dead he was not tangible. He had a physical body, that was bound to Sauron's power as long as Sauron's power (the Ring) was still in existance. And as can be seen on the Pelennor fields his physical self could be destroyed. Where hte King of the Dead had no physical body, and was 'barely visible.'
In conclusion this means, that the King of the Dead could not physically kill the Witch-King, it was not something he was capable of doing. The only way he could defeat him would be to send him fleeing, but why would the Witch-King fear the very fear that he uses? And the Witch-King could not physically kill the King of the Dead, because the King of the Dead did not have a physical body, he was a 'spirit,' and that in Tolkien cannot be destroyed. So, it would be a draw.
