Joel's thesis is that crufty old code has bug fixes in it that will be inadvertently unfixed in a rewrite. He concedes the point that rewriting is much faster than heavy refactoring.

Experience says Joel is wrong. The old code is a mess because people got lazy or weren't quite sure what direction they were going, not because it accumulated value as bugs were fixed. This other guy is right. If the experts on the current code think it's faster to rewrite than go through a todo list on the current code, they're probably correct.

I think you can likely make the decision by empirical means. How many moving parts and roughly how much code can be removed in a rewrite?