[Boromir88]

Im going to go back to some earlier points by narfforc as I think he is dead on. From the text we see that Gandalf proved greater than the Witch-King in two ways.

First, Gandalf proved indeed to be the 'greater' when it came to power. The Witch-King comes bursting through the gate, Gandalf is the only one who stands in his way (completely unafraid) and ready to confront him. The Nazgul's greatest weapon (we are told) is their fear, and they have 'no great physical strength against the fearless.' (Letter 210). The Witch-King naturally plays to his greatest asset...fear. This doesn't work as Gandalf is unafraid and even intent on chasing after the Witch-King had Pippin not come and told him about Faramir.

The second way is that Gandalf proved to be the better commander. To expand on what narfforc said, who was it that healed Theoden? Who was it that got the Rohirrim to fight against Saruman and ultimately come in to save the day? Who was it that instructed the Rohirrim to go to Gondor's aid and hence their arrival catching Mordor off guard, and the Witch-King to flee as the Rohirrim came up on the flank? Gandalf.

So, Gandalf not only overcomes the Witch-King's greatest weapon (fear), but also proves to be the better commander as The Witch-King is caught off guard by Rohan's arrival. Gandalf in both ways proves to be greater, and I cannot see how anyone cannot claim that in the confrontation with the Witch-King that Gandalf did not get the better of him.