Gandalf's power was greatest when it was needed to guide and protect, the narrative always indicated that although his role is vital to the survival of the free peoples, his fate was never to overcome the dark adversary(s) himself. Not only that but, it's stated very early on that the fate (and power) of the Nine is bound to Sauron, so it would follow that the Witch King's-king's power was at its apex at the siege of Minas Tirith, when Sauron's might (albeit greatly diminished without the Ring) was at its greatest since his fall at the hands of Isildur.
My interpretation is that the destruction of Gandalf's staff by the Witch King-king fits entirely to the narrative. The most common theme to the storytelling in both The Lord of the Rings and The Hobbit is that 'small is not necessarily weaker than big', so Peter Jackson's dramatic attempt to emphasise the strength of will of Merry, Éowyn and Sam and Frodo is not misplaced.