Gandalf is one of the Heren Istarion, the Order of Wizards and is great among the Ainur. The Witch-king is the Lord of the Ulairi and was probably of Numenorean race.
In Eregion, outside the West Gate of Moria, Sauron came as Annatar, Lord of Gifts and seduced the Gwaith i Mirdain and forged the Rings of Power. After Giving the Nine to Men he made The One Ring to be master of them all and after a time, the Men who possessed the rings became slaves to the One being invisible to eyes and wielding great fears. All this most of you know, but I am trying to compare the power of Mithrandir Gandalf and the Witch-king, Lord of Morgul.
It is ironic that in the book, the greatest of the servants of Sauron is destroyed by a Hobbit. In the book the Witch-king is described as a sorcerer, king of Angmar, shadow of despair and all other things denoting power and malice. Theoretically, Gandalf being of the Maiar, a superior race of angelic spirits before the world and the Witch-king wielding a Great Ring, but being a Man in origin, doesn't it make more sense that Gandalf has the greater power. He drove the Morgul-lord away from the Gates of Minas Tirith in the Siege of Gondor, he throw down the Balrog upon the pinnacle of Zirak-zigil, and he chased away the Nazgul with a ray of white light when they were escaping Osgiliath, all of these aspects are signs of his power. According to the Silmarillion (my personal favourite book) Olorin (Gandalf in Valinor) was the wisest of the Maiar, and being of the people of Manwe and Varda, he should be along with Eonwe and Ilmare one of the greatest of the Maiar, comparing himself to Sauron maybe. In Unfinished Tales, there is a part in The Istari chapter about a Valinorean Council about what is to be done about Sauron and Olorin is summoned. Olorin says that he is too weak to contest with the power of Sauron and that he fears him, but Manwe replies that it is all the more reason that you should go. This fear is (I believe) for the Elves and Men not because of weakness and is also because of the nature of that once great Maia Sauron. Like Morgoth, his former master, he became as it seemed, a Dark Lord, being lord of orcs and trolls and other lesser creatures of Morgoth. After the downfall of Numenor (caused partly by Sauron) he was sucked into the sea but escaped and found his way back to Mordor as a cloud of shadow, so his fair hew was removed from him. After his next downfall, at the Battle of the Last Alliance, his actual physical form was vanquished and he became a mere spirit of malice lost in the Wild or Far Far East and when he returned to Dol Guldur and thence to Barad-dur, he lurked in his Dark Tower Lugburz gnawing at plans of bitter revenge and cursing the Dunedain and the Elves in vain sending forth legions of Orcs and the dreaded Witch-king to terrorise the Men of Gondor. Gandalf, however, clad in a body of a man wished to possess neither wealth nor slaves and therefore had the greater wisdom and strength of will.
The Witch-king, received the title 'Witch-king' when he was Lord of Angmar, a region in the far north of Middle-earth by the northern peaks of Hithaeglir in the mid Third Age of the Sun. Angmar was built as a threat to the Dunedain of Arnor because Arnor was out of the reach of Sauron in his far southerly dwelling in the Land of Shadow. I don't know what the Wizards were doing at this time, but they can't have been doing much! Anyway, I think that Gandalf could have trounsed the Witch-king!