Gandalf also wears a Ring of Power, and 1 of the 3 Elf Rings no less, greater than any of the 9. So he wins there.
Yes, his power was limited while he was Gandalf the Grey, but now that he has been sent back by Eru he can use most of his strength, except for some things like the ability to shapeshift. So the limited power argument is basically out as far as I'm concerned. Let us not forget he defeated an evil Maiar who was using his full strength, that being the Balrog, and that was while he was Gandalf the Grey.
Gandalf has been alive since THE BEGINNING OF TIME, there is no way he has less combat experience than the Witch King, argument out of the question.
The prophecy is that the Witch King cannot be killed by any MAN, but Gandalf is not a man, he is a Maiar. Argument out of the question.
Not going to get any more involved than this, because I don't think the presenter of the idea should argue a point, and should remain neutral. I personally think that neither would kill the other, but that it would be an incredible fight ending in a stalemate.