I think a hint as to what would have happened in a duel between the Witch-king and Galadriel can be found in the the following passage. If I remember correctly, two of the Nazgul, including Khamul, the WK's second in command, led the attack on Lorien from Dol Guldur.
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Three times Lorien had been assailed from Dol Guldur, but besides the valor of the elven people of that land, the power that dwelt there was too great for any to overcome, unless Sauron had come there himself.
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If an army led by two Nazgul couldn't overcome Galadriel's power, I don't see how the Witch-king could have either.
As for Gandalf, recall that at Amon Sul, he fought off
all nine of the Nazgul together, and even then they waited till after nightfall to face him. And that was before his powers were upgraded following his duel with the Balrog. So I don't think the Witch-king would have had any better luck against Gandalf single-handedly at Minas Tirith.
Peter Jackson's misleading portrayal notwithstanding, the reason that Gandalf didn't fight the Witch-king wasn't his inability to do so. Rather, if he were to openly fight the Witch-king, his supernatural abilities would become apparent. Even though he was permitted to use them a little more openly, he didn't want to do so unless absolutely necessary.
Fortunately, events conspired (through Eru's grace?) to prevent this from happening. First, the Rohirrim showed up in the nick of time, and the Witch-king had other matter to attend to. Then Pippin convinces Gandalf that he must intervene to save Faramir, and by the time that situation is resolved, the Witch-king is no more.