Given that MWI uses the mathematical formalism equivalent to CI, they are equivalent in the only respect that counts. For example, neither provides any testable predictions re alternate universes, except that they are not observable. Of course, the MWI model tends to make people feel good about Quantum Mechanics, but that is a purely psychological effect.
CI has wave-form collapse. This isn't used in the mathematical formalism because there's no specific point at which it's agreed to happen. It's just assumed that it is when the system gets "macroscopic".
They do show evidence of alternate universes, and they are not unobservable. For example, the double-slit experiment has two pasts. One for each slit.
Also, according to timeless physics, the past and future is just alternate universes. If you believe the past exists, and you accept the basic idea, you believe that alternate universes exist.
I am looking for examples of mysterious answers that were eventually explained *away* by science. I can think of two: One is the belief that the behaviour of living things was explained by the mysterious force of elan vital, and not by mere chemistry; which was destroyed by the synthetisation of urea. The other is the special (and mysterious) role of the conscious observer in quantum mechanics, which was explained away by demonstrating that rocks can get entangled with electrons just as much as brains can. Can anyone furnish me with other examples?
I observe in passing that phlogiston is *not* such a mysterious answer. Eliezer is down on it, but I think unjustly so; for people did in fact perform experiments on phlogiston, including the final experiment to find the weight of the phlogiston that had passed out of the burning material and into the byproducts. It turned out that the phlogiston had negative mass... in other words, that the direction of the transfer had been misidentified. But if you think of phlogiston as `negative oxygen', it makes the same predictions as modern chemical theory. This is no worse a mistake than mistaking the direction of the current, a mistake which is *still* enshrined in our sign conventions; it is not a mysterious answer of the form "X->Y" with no details of X given and any value allowed for Y.
However, I digress. Mysterious answers blown away by experiments, anyone?