Based primarily on what Tolkien says in his
Letters, I would agree with
obloquy that Gandalf was Sauron's equal. Although I would rule such evidence as inadmissible, or at best of little persuasive value, in interpreting the films as the "book" facts relevant to this are not part of the film story.
Nevertheless, I think it is fair to say that, in the films, Gandalf is portrayed as more powerful as the Witch King. But does this really mean that it is ludicrous to have Angmar (
) seemingly better Gandalf, and to have Gandalf show fear, in this scene? After some consideration, I don't think that it does. There are numerous examples in Tolkien's works, many of which are carried over into the films, of characters defeating those who are clearly superior in power. I would class Eowyn and Merry combined as less powerful than the Witch King, yet they defeated him. And Wormtongue (in both book and EE) was able to kill Saruman. Circumstances count for much. Perhaps, given all that was going on in his mind (directing the defence of Minas Tirth, riding to the aid of Faramir, not to mention thoughts of Frodo's desperate journey), Gandalf's mind was momentarily distracted and the Witch King was able to seize the initiative. Gandalf's fear is also justifiable. If it was possible for the Witch King to defeat him (and, given the precedents noted, I believe that it was), there was much at stake. If Gandalf fell, Minas Tirith could fall. And that could well bode darkly for Frodo's Quest and the fate of Middle-earth itself. A fear of failure in these circumstances is understandable. Moreover, since Gandalf is not portrayed as a Maia in the films, it is plausible that he was subject to the Witch King's main weapon - fear - even if less so than "ordinary" Men.
Finally, who is to say that, in the film, Gandalf would not have rallied his powers and defeated the Witch King, or at least driven him off, had the Rohirrim not arrived? Perhaps the Witch King feared this, which is why he did not finish Gandalf off when he had the chance. We cannot be sure, just as we cannot be sure what the outcome of the encounter would have been at the Gate in the book, but for the arrival of Theoden's Riders.
Now I doubt that any of this went through the film-makers' minds. My only point is that this scene
can be explained and justified, in film terms. It is not inherently ludicrous (in the same way, for example, as having Denethor run all the way from Rath Dinen to the front of the Citadel and fall off the edge while on fire).
As to Glorfindel's prophecy, I agree that there is a difference, in theory at least, between prophesising that someone
will not die at the hands of a Man and saying that they
cannot die in this way. Glorfindel's prophecy in the book is of the former category, but the prophecy in the film falls into the latter category. Gandalf says that there are those who say that no man can kill the Witch King. The suggestion in the film, therefore, is that he is impervious to attacks by Men. Assuming that, in the films, Gandalf is a Man, this gives Gandalf even more reason to fear him.