Assuming they don't make any approximations other than collapse, yes a classical computer simulating Copenhagen takes fewer arithmetic ops than simulating MWI. At least until someone in the simulation builds a sufficiently large coherent system (quantum computer), at which point the simulator has to choose between forbidding it (i.e. breaking the approximation guarantee) or spending exponentially many arithmetic ops.

Copenhagen (even in the absence of large coherent subsystems) does not take significantly less memory than MWI: both are in PSPACE.

Otoh, if the simulator is running on quantum-like physics too, then there's no asymptotic difference in arithmetic either. And if you're not going to assume that the simulator's physics is similar to ours, who says it's less rather than more computationally capable?