In non-relativistic MWI, the evolution of the quantum state is fully described by the Schrodinger equation. In most other interpretations, you need the Schrodinger equation plus some extra element. In Bohmian mechanics the extra element is the guidance equation, in GRW the extra element is a stochastic Gaussian "hit".
In Copenhagen, the extra element is ostensibly the discontinuous wavefunction collapse process upon measurement, but to describe this as complicating the math (rather than the conceptual structure of the theory) is a bit misleading. Whether you're working with Copenhagen or with MWI, you're going to end up using pretty much the same math for making predictions. Although, technically MWI only relies on the Schrodinger equation, if you want to make useful predictions about your branch of the wave function, you're going to have to treat the wave function as if it has collapsed (from a mathematical point of view). So the math isn't simpler than Copenhagen in any practical sense, but it is true that from a purely theoretical point of view, MWI posits a simpler mathematical structure than Copenhagen.
In other words, MWI says: apply Copenhagen for anything useful.
http://www.scottaaronson.com/blog/?p=1103
Eliezer's gung-ho attitude about the realism of the Many Worlds Interpretation always rubbed me the wrong way, especially in the podcast between both him and Scott (around 8:43 in http://bloggingheads.tv/videos/2220). I've seen a similar sentiment expressed before about the MWI sequences. And I say that still believing it to be the most seemingly correct of the available interpretations.
I feel Scott's post does an excellent job grounding it as a possibly correct, and in-principle falsifiable interpretation.