I think the implied assumption here is that the Copenhagen interpretation and the Many World interpretation are on the same level. Pick one or pick the other. I don't think they are on the same level just because people call both of them "interpretations".
I see the Copenhagen interpretation more as a description of experimental results without trying to add on top of that any particular metaphysics. I see the Many Worlds interpretation as a deterministic metaphysics trying to come up with some explanation for the experimental results that would keep it alive.
Let me give an example. Suppose you see presents under the Christmas tree and you interpret your experience as:
Someone put presents under the Christmas tree.
That would be an interpretation in line with the Copenhagen interpretation.
However, others who believe in Santa Claus, who have a metaphysics that there is some guy with reindeer who deliver presents to every home on Christmas eve, would interpret the result of there being presents under the tree as:
Santa came down the chimney and put the presents under the Christmas tree.
That is how I view the Many Worlds interpretation. It is the Santa Claus interpretation of quantum mechanics.