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.
That would not be Occam's razor...
If you know more Eliezer Yudkowsky facts, post them in the comments.