And from what I have read I can tell that the sentence - "despite the lack of testable predictions differing from the Copenhagen interpretation" - is not correct, or at least not crucial.
It is correct, and it is crucial in the sense that most philosophy of science would insist that differing testable predictions is all that would favor one theory over another.
But other concerns (the Bayesian interpretation of Occam's Razor (or any interpretation, probably)) make MWI preferred.
An interpretation of Occam's Razor that placed all emphasis on space complexity would clearly favor the Copenhagen interpretation over the MW interpretation. Of course, it would also favor "you're living in a holodeck" over "there's an actual universe out there", so it's a poor formulation in it's simplest form... but it's not obvious (to me, anyway) that space complexity should count for nothing at all, and if it counts for "enough" (whatever that is, for the particular rival interpretation) MWI loses.
If you know more Eliezer Yudkowsky facts, post them in the comments.