This is a very active topic in quantum mechanics (and also in philosophy, somehow), and there is no clear answer. Both interpretations have pros and cons. I don't know well enough Everett's work (and its more recent, modified, incarnations) to have a fair judgement on that, so that I prefer to pass. Data-wise (data always wins), both interpretations are fine and until they will be tested against each others, we won't be able to tell. Note that there are ways to distinguish both experimentally, but I don't remember the details (and this is probably not that easy as not done already).

Note that this is slightly off topic relatively to the present post, and this is not really what I am working on (I am not working on the foundation of quantum mechanics).