This question originally appeared on Quora. 
Answer by Danielle Maurer, Anthropology Major & SciFi Fan
I'm going to take a stance and say that no, the Witch King is not more powerful than Gandalf.
Gandalf, like Saruman, Sauron, and several other characters in the greater Lord of the Ring universe, is a Maia. The Maia are spirits that came into being at the beginning of time. They are lesser in power than the fourteen Valar, but still very potent beings. The Maiar typically associated themselves with a Valar. For instance, Eonwe is the herald of Manwe, and Sauron was corrupted and became Morgoth/Melkor's lieutenant. Gandalf is one of the five Maiar sent by the Valar to contest Sauron. Thus, Gandalf is a being that has existed since the beginning of time. He may wear the flesh of an old man, but his spirit is ancient and powerful - and he is not and never has been mortal in any sense. Even more, Tolkien wrote that Saruman knew Gandalf was wiser and more powerful -- and hated him for it (see the wiki article on Gandalf).
Now let's look at the Witch King, leader of the Ringwraiths. He was originally a mortal man who accepted a ring of power from Sauron and was corrupted into darkness. Admittedly, he was a sorcerer and evidently an able battle commander. He ruled Angmar and was Sauron's second-in-command, but ultimately the majority of his power is derived from Sauron.
The confusion on this question likely stems from the movie version of events, where the Witch King breaks Gandalf's staff at Minas Tirith. We will ignore this version of events, since it looks nice on screen but is not necessarily true to Tolkien's universe.
If we look at the book version of events, when the Witch King shows up at Minas Tirith, Gandalf is the only person who can resist him. Despite the Witch King calling him an old fool, Gandalf is prepared to stand and fight. Although other events prevent them from duking it out, by knowing their respective origins, we can fairly easily to predict that Gandalf, as a divine and ancient being, would probably be able to triumph over any sorcerer that began life as a mortal man. Admittedly, the Witch King takes some power from Sauron, but of necessity it is less than Sauron himself possesses (which may or may not be enough in its entirety to destroy Gandalf the White, but definitely is not when only a fraction is brought to bear).
Moreover, let's look at what Gandalf accomplished before he became Gandalf the White and his powers increased. Gandalf went toe to toe with a Balrog and (ultimately) came out on top. The Balrogs, like Gandalf and Sauron, are also Maiar. Thus, we can deduce that Gandalf is certainly not at the bottom of the Maiar power ladder - and after his return is probably closer to the top than the middle.
Gandalf also fought an undisclosed number of the Nazgul at Weathertop. How many this included (and whether the Witch King was there) is uncertain, but there is a possibility that it was all nine, and he fought them to a draw. Again, this is before he became Gandalf the White and got even more powerful.
Ultimately, we can't know for sure, as Gandalf himself admits that the Witch King may be able to overpower him (although this would have to be with the full force of Sauron's backing). But I think the evidence strongly supports Gandalf as the more powerful being.
Gandalf also has in his possession one of the three elven rings of power: Narya, the Ring of Fire. How much help Narya would be in a confrontation is debatable, but I doubt that it could be left entirely out of the power calculations, and would be another significant mark in Gandalf's favor.
Some relevant LotR wiki links:
Witch King: http://lotr.wikia.com/wiki/Witch...
Gandalf: http://lotr.wikia.com/wiki/Gandalf