What particular gold-standard "Occam's razor" are you adhering to, then? It seems to fit well with "entities must not be multiplied beyond necessity" and "pluralities must never be posited without necessity".
Note that I'm not saying there is no gold-standard "Occam's razor" to which we should be adhering (in terms of denotation of the term or more generally); I'm just unaware of an interpretaton that clearly lays out how "entities" or "assumptions" are counted, or how the complexity of a hypothesis is otherwise measured, which is clearly "the canonical Occam's razor" as opposed to having some other name. If there is one, by all means please make me aware!
The MWI requires fewer rules than Copenhagen, and therefore its description is smaller, and therefore it is the strictly simpler theory.
If you know more Eliezer Yudkowsky facts, post them in the comments.