If this is true, why doesn't this count as straight-forward induction? It certainly looks like induction and if it is, why is this a philosophical rather than scientific case? Also, if we think CI and MWI make the same predictions what does it mean to say "tended to be more correct"? Doesn't that require experimental evidence falsifying one of the interpretations at a later date?

It is not scientific induction, since you can't measure elegance quantitatively. However scientists have subjective intuition based on the successes and failures of past other physical theories. This is what I meant by "philosophical edge".