Many-worlds - which starts with being a lot more rigorous about what 'measurement' is (entangled yourself with the system in question) is much simpler than either, I think.
My general impression is that Many-Worlds is getting more popular as physicists make precise how entanglement, measurement, and decoherence exactly work. I think it'll supplant Copenhagen as what we teach in intro classes eventually. But this is just my impression from the physics blogs and papers I've read; I'm not a physicist myself.
I can't speak for De Broglie-Bohm, but it would seem that theory also have a similar strike against it: the math is more complex than the equations QM physicists are familiar with. It's just not the simplest theory that fits the observation.
The obvious alternative is to just stick to the math. Problem is, the simplest math that explains our observations implies a universe that forks all the time. For some reason, possibly the intuition of a unique universe, many people cannot accept that.
I'm not a physicist, but doesn't classical QM have the problem of the "collapse of the wave function", i.e. "suddenly" Schrödinger's equation does not hold anymore - a problem that the De Broglie-Bohm theory does not have? Shouldn't this be considered as a strong sign against "typical" QM formulations and for the De Broglie-Bohm theory?