Gandalf the White was too powerful for the Witch King. Jackson really screwed up on that scene. The Witch King may have believed he could defeat Gandalf, but he was wrong and knew not who and what he faced. Gandalf could not destroy the Witch King but he would have at least chased him off if not destroyed his current form. Gandalf had already ridden out against many Ring Wraith and rescued Faramir from them.
Gandalf the White was a greater being by far, when Eru sent him back he was no longer required to hide his true self as Gandalf the Grey. Gandalf the White was much closer to Olórin as he was in Valinor. Against he no phantom of the enemy could stand for long.