For example, the Sleeping Beauty problem is very puzzling if you insist on thinking in terms of subjective probabilities, but becomes completely clear once you introduce a payoff structure.

Heh, I was just working on a post on that point.

Believing in one formulation of a theory over a different equivalent formulation isn't likely to win a Bayesian reasoner many dollars, no matter what observations come in. Therefore the reasoner should assign degrees of belief to equivalence classes of theories rather than individual theories.

I agree that that is true about equivalent formulations, literally isomorphic theories (as in this comment), but is that really the case about MWI vs. Copenhagen? Collapse is claimed as something that's actually happening out there in reality, not just as another way of looking at the same thing. Doesn't it have to be evaluated as a hypothesis on its own, such that the conjunction (MWI & Collapse) is necessarily less probable than just MWI?