I love Lord of the Rings," and the Witch-king of Angmar is maybe my favorite character from it, so I will expand upon what is known of him. He CANNOT be hurt by a man (let's assume that he does), not under normal circumstances. If Darth Vader counts as a man, he would have to have his lightsaber blessed by Elves in order to harm him. Also, the Witch-king's body under his robes is invisible, so if he took off the robes and disarmed himself, he could a particularly nasty spell he has on Vader (before Vader could attack him - doubtless he would sense him nonetheless, but if the foe is unseen it makes it slightly harder; actually, maybe not, seeing as Vader is so in touch with the Force and would probably sense him immediately, assuming the Witch-king had negative Force energy emanating from him - I'm going to assume that this is happening where bad guys give off evil Force energy).
Anyways, that's it. However, both characters, respectfully, are cool as Hell.
I dont like these topics, cause both characters exist in different universes with different rules, but since i got nothing else to do...
Thw Witch King would win, because in LOTR the villains are gods and spirits, they are the figures of everything the universe is made off. While Vader uses the Force, connected to all things. If he was in Tolkien's universe, Vader only has a superficial use of the spiritual energy of things, while Sauron and the Witch king ARE the spiritual force.