Good question. It will probably never be answered, since it’s likely nobody will ever try it. One precursor to my research with The California Energy Commission was just such a counterrotating dual-rotor setup. It was supposed to use a counterrotating generator, with the rotor and “stator” spinning in opposite directions. But, well, you know, that would have been too hard to do, so, once funded, the project was watered-down to use two separate generators, since the “Professor Crackpots” of the world are unlikely to have the design and fabrication ability to construct a working counterrotating generator.
Since the main stated advantage was the increased relative speed of the generator, that “research” never embodied its main feature. As far as I remember, it went nowhere.
There are plenty of drones out there using counterrotating propellers, usually, or maybe always, using two separate motors. If there was a significant efficiency advantage to counterrotating rotors in a wind turbine, you’d think we’d have heard about it by now. Since a regular rotor is capable of approaching Betz, there’s not much room for improvement, but theoretically some energy lost to wake swirl could be recovered. One main goal in wind energy is to reduce complexity so there is less to go wring. Every moving part and wear point must be eliminated to the extent possible to achieve that 20-year lifespan! 
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