There is no difference at the level of predictions, because I’m not calling for any new laws of physics beyond QM. It’s a matter of what makes sense as interpretation.
The reason for that lack of difference is that every interpretation of a physical theory is an attempt at reifying the theory in some sense. Each interpretation must conform to the theory at every level of examination since the interpretation is an ascription of a certain ontology to that theory, not a modification of that theory. But it isn’t the ontology which predicts things, it’s the model which we’ve attempted to reify that does that, so no amount of experimentation is going to reveal any difference between two interpretations of the same theory. Nonetheless, those two interpretations are not equivalent. I cannot find, by way of experiment, any difference between any two interpretations of quantum mechanics, but we need only find one which asserts the metaphysical reality of wavefunctions and one which does not to see that they do not, in fact, entail precisely the same body of claims and are therefore not equivalent.
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