Is the Witch King afraid of Gandalf?
People get a little too bogged down in the details of the nature of different types of characters, and miss their purpose.
Gandalf the White is one of the Istari, which is to say he's a Maia, basically an Angel who took on a human-like form, that burdens him with the needs of life like sleeping, eating, drinking, weariness, etc. He is the most powerful servant of the Valar, and through them of Eru Illuvatar, in Middle Earth at the time of the War of the Ring. It was Eru who sent him back, enhanced with greater power, and resurrected him after his death fighting the Balrog, as Tolkien says in letter 156 of the Letters of JRR Tolkien.
In History of the Lord of the Rings, Christopher Tolkien provides some notes from his father composed at the time he was writing the chapter "The White Rider," in which Gandalf reappears. The notes include a mention that Gandalf returns as "the White Wizard," and that he possesses "some measure of the power and dread of the Ringwraiths, but for good instead of evil."
The Witch-King, Lord of the Nazgul, is the greatest of Sauron's servants in Middle Earth. He is a Ringwraith, the twisted spirit of a human enslaved to one of the Nine Rings. He is essentially an undead creature, filled with the wrath and hatred that Sauron holds for all those that oppose him.
Where the Ringwraiths go, especially when they are gathered under their captain, they spread fear and terror and a sense of hopelessness. And the Ringwraiths are often referred to as Black Riders.
Where Gandalf the White goes, he spreads hope, joy and courage among those fighting for good, but he is a terror to the servants of Sauron. As Aragorn says, "The Dark Lord has Nine. But we have one, mightier than they: the White Rider."
So is Gandalf "stronger" than the Witch-King? Sure, though the Witch-King remains a powerful and dangerous enemy that Gandalf would not under-estimate, and it's not always the case that the strongest opponent wins a fight. But you can focus too much on the nature of these beings... Maia vs. Shadow of a Man... and lose track of what Tolkien was trying to accomplish in setting them against each other.
Gandalf serves as the counterpoint to the Nazgul... their opposite within the story. What they are to the forces of evil, he is to the forces of good, and his power can counteract the fear and terror that strikes those who try to fight them.
Gandalf's purpose is not to destroy the Witch-King, or the rest of the Nazgul, or even Sauron himself, through the power that is in him.
Gandalf's purpose is to enable others to resist and ultimately defeat them. He is the light set against the shadow. He is the bringer of hope.
Think about it: what role does Gandalf play in the downfall of the Witch-King? Does he slay him with the power that is in him? No. But his death is still very much Gandalf's handiwork.
At the Council of Elrond, Gandalf convinced Elrond to include Merry and Pippin in the Fellowship, rather than sending them home to the Shire. So Merry was there on the battlefield, ready to assist Eowyn with a Numenorean blade woven with spells for the defeat of Angmar, the Witch-King's former realm.
In Rohan, Gandalf healed Theoden, and instilled in him and his people the courage to fight back first against Saruman, and then against Sauron. If not for Gandalf's actions, Rohan would never have ridden to the aid of Gondor.
It was the blowing of the horns of Rohan that caused the Witch-King to leave the Gates of Minas Tirith. This by itself shows how much more "powerful" Gandalf was than any of the Nazgul... his actions had set in motion a chain of events they did not anticipate, which forced the Lord of the Nazgul to withdraw from the city almost in the moment of his triumph.
And where did the Witch-King go? To confront Theoden, who was there because Gandalf had healed and inspired courage and hope in him. Yes, he defeated Theoden, but in so doing, he motivated Eowyn to stand and oppose him, to defend her fallen lord and the man she thought of as a father... and just as he was about to crush her, Merry stabbed him in the back of the leg with that blade. Merry, who also would not be there if not for Gandalf.