In my opinion it doesn't make much sense to discuss which one is correct, providing that both fit to all observations.
Quantum mechanics is a theory in physics, which allows us to describe lots of observations, which we couldn't explain before, in a mathematical way. So given certain beginning state it, defined by some observables it gives us the probability that we end up in a certain other state. Here, talking about probabilities and the fact, that a certain amount of intrinsic uncertainty makes it impossible to determine a state exactly (meaning, that, providing we have a measuring device which is able to do measurements with the required accuracy, we can't know all properties with arbitrary accuracy at the same time), appears a difference between other classical theories and QM. The way how QM describes world doesn't really match with human's conception how things happen in real life. This is the point, where interpretations arise.
If you compare to classical mechanics and try to interpret the result: "At t=0 mass m was at x=0 and has velocity v = 2. At t = 2 mass m was at x = 4", I guess there is just one way people might interpret this result, because that's a situation we know very well from our real life. If we take a look at t = 1 we are quite sure to find mass m somewhere between x = 0 and x = 4 (depending, whether there is some acceleration). Interpretations, which claim, that the mass somehow tunnels between x = 0 and x = 4 turn out to be wrong in this way. So I would say in classical mechanics there is only one widely accepted interpretation.
Now in QM we basically can't say what happens between two points, where we take measurements. That's an intrinsic part of theory.
In my understanding, interpretations are just a way of how humans try to translate results of QM theory to the language their brains work. Of course, different people might have different ways of translating the same results in their brain's language. An interpretation, that goes confirm with all observation made is "correct". If it fits to the mindset of many other people, it is widely accepted, if not one's interpretation is a quite unpopular one.
So answering your last question: I don't know any observation, which is made by one, but not by the other, it only might be easier to describe one certain observation in one interpretation, than in the other one. If a difference would arise, I would call the interpretation, which doesn't match with observations, a wrong interpretation.
I hope that gave you some new starting-points to think about. As the word "interpretation" suggests, there might be not be the only way to think about it and due to it is somewhere in the intersection between physics and philosophy it's worth to discuss about it.
