Gandalf Vs. The Witch King

[Inziladun]

If the Balrog was 'greater', why is it that Gandalf was the one who returned, after throwing his enemy down a mountain?
I really don't see the merits of an argument about the WK being superior to Gandalf. The Morgul-lord was a Man fundamentally. Physically and spiritually he had been altered drastically by Sauron, but those changes ultimately diminished him. Gandalf explains the effects of a Ring of Power on a mortal:

'A mortal, Frodo, who keeps one of the Great Rings, does not die, but he does not grow or obtain more life, he merely continues, until at last every minute is a weariness.'

Perhaps, through the WK's utter submission to the will of Sauron, he was able to 'borrow' some of Sauron's power occasionally, such as the words of 'power and terror' that helped break the Gates of Minas Tirith.
As Tolkien said in one of the Letters, the WK there had been given an added 'demonic force' by being placed in command by Sauron. But even with that additional power, he does not (in the books) rise to Gandalf's challenge, or attempt to ride past him into the City? Why not? Certainly, the Rohirrim had just arrived, and Sauron's forces had a new army to fight. All the same, if the Morgul-lord had gone into the City then, leading his forces, I think they could have taken Minas Tirith.
So why did the Witch-king not do so? He lacked the power. Instead, he runs away and, as Morthoron noted, gets offed by a woman half his size, and a Hobbit probably a quarter his size.