So, I'm reading Max Tegmark's Our Mathematical Universe (Knopf edition, p. 229). He's discussing Everett/MWI for a bit and I'm not really paying attention and then I wake up to this:
[I]t's time to update the quantum textbooks to mention decoherence (many still don't) and to make clear that the Copenhagen interpretation is better thought of as the Copenhagen approximation: even though the wave function probably doesn't collapse, it's a very useful approximation to do the calculations as if it does collapse when you make an observation.
Now, I believe I have read (elsewhere, e.g., on this site) that these interpretations do not make any difference whatsoever* when it comes to predictions. But here, apparently (at least that is how I read the above), it is claimed that MWI and Copenhagen actually differ in predictions (and that MWI has the right predictions). Is that correct? (This would make it slightly more difficult to be agnostic about choosing your favourite interpretation for the time of day, right?)
NB: I'm not specifically asking whether the wavefunction collapses or not.
*As in: zip, nada, zilch, exactly $0$.