EY's very attractive intuition that of two theories making the same predictions, one is true and the other ... what? False? Wrong? Well, ... "not quite so true".

"More Wrong". :)

I can think of two circumstances under which two theories would make the same predictions (that is, where they'd systematically make the same predictions, under all possible circumstances under which they could be called upon to do so):

• They are mathematically isomorphic — in this case I would say they are the same theory.
• They contain isomorphic substructures that are responsible for the identical predictions. In this case, the part outside what's needed to actually generate the predictions counts as extra detail, and by the conjunction rule, this reduces the probability of the "outer" hypothesis.

The latter is where collapse vs. MWI falls, and where "we don't know why the fundamental laws of physics are what they are" vs. "God designed the fundamental laws of physics, and we don't know why there's a God" falls, etc.