Collapse theories can do something many worlds can't do: they can make the predictions! As can Bohmian theories.

Many worlds, like at least one other prominent interpretation (temporal zigzag), is all promise and no performance. Maybe Robin Hanson's idea will make it work? Well, maybe Mark Hadley's idea will make the zigzag work. Hadley's picture is relativistic, too.

Many worlds deserves its place in the gallery of possible explanations of quantum theory, but that is all.