The laws of the very small (quantum mechanics) work well on their own, and the laws of the large (classical physics) work well on their own as well. The difficulties (and most of that long list of weird effects) come from the interplay between the big and small laws. For example, in quantum mechanics things can be in multiple locations, but in classical physics they clearly can’t. Each of those different versions experiences a different classical (seemingly non-quantumy) world. So (to finally answer the original question) the two interpretations differ in their experimental predictions only for larger systems.