I've had several people ask for a more detailed critique of Nibley's response.
In a nutshell, he didn't address Brodie's best arguments or sources (I readily admit that there are some flaws in Brodie's work--a few of which Hugh points out). Essentially, a rebuttal that doesn't focus on the key, major points isn't much of a rebuttal IMO. Anyone can point out a few flaws in just about any book, but that doesn't mean that everything the author wrote should be 100% disregarded.
Hugh also spent much of the response (and the other essays in "Tinkling Cymbals and Sounding Brass") doing ad hominem-type attacks, making fun of those who don't agree with his religion, and being obnoxious--rather than refute the potent points on the problems of Mormonism. This is his style I guess, but it doesn't make for a very good, scholarly rebuttal. For his full commentary see this page.