Yes, I've read that one as well. It was a while ago, but from what I remember, it was higher-level than the Smith book. The Smith book is basically a normal mathematics curriculum book, not a "pop science" book (not to say that N&N is), which works out theorem after theorem to get to Godel's proof. Also, it starts off with computer-science proofs instead of the original Godel proofs, which many in this audience will probably prefer.
One thing I love about N&N is that it's short (160 pages) and the paperback is cheap ($7.65) so that I have no compunctions in lending it out.