Yes, but they don't differ on how you deal with practical problems, at least not ones on the level of how to design a car or a computer. Maybe they would affect cutting edge semiconductor research or fusion reactor design, (I don't think the interpretations of quantum physics do, but other conjectures might).

I figured someone might mention this. (I almost addressed it in my original comment, but it was a bit peripheral to my main point.) The various quantum interpretations are not schools of physics thought; every physicist "believes" in quantum mechanics. They are schools of thought on the interpretation of quantum mechanics---which certainly is an indication of that (sub)field's intellectual immaturity. And, like economics, the interpretation of quantum mechanics has more than its share of bullshit. As Stephen Hawking supposedly once said, "When I hear of Schrödinger’s cat, I reach for my gun."

N.B. I predict the rise of quantum decoherence theory will change this picture in fairly short order.

I consider the silence of the Copenhagen interpretation over what happens during measurement to be an actual difference of physics, not of interpretation. If some other theory were able to predict, say, the time it takes for a wave function to collapse, or the number of particles another must interact with for it to decohere, or so on, it's a difference in predictive capacity, not merely of metaphysics.

That's a good point. There is definitely some physics content in the interpretation of quantum mechanics---Bell's Theorem certainly took many physicists by surprise when it came out, since it proved people were arguing over more than words---but in any case it's all a tiny higher order term in the series expansion for 'physics'. (The 0th order term is "Newton", FWIW. ;-)

Those tiny terms matter when things go nonlinear! ;-)

Interpretation of quantum mechanics is outside of the scope of physics, it's more like philosophy or something. For physics to be like economy in that respect, there would have to exist, for example, university professors who still wouldn't believe special relativity or quantum mechanics and claim that only the classical newtonian mechanics makes any sense.