What are the advantages of dual counter-rotating rotors vs coaxial rotors?
Counter-rotate Picture above from this answer, which compares the Chinook with the V-22 Osprey, another counter rotating twin rotor.

For a given weight, the larger the rotor the less power is required for generating the necessary thrust. And here is where a single rotors' advantage is, one single rotor requires less power than two rotors with half size each. In the hover, the single rotor throws away about 10-20% of the engine power to drive the tail rotor, but in cruise flight much of that torque compensation is generated by the vertical tail.

Yes the payload location range of the Chinook config is without equal. In case of one engine failure, the remaining engine can drive both rotors since they are coupled by a shaft. Autorotation is not an issue either - from this thread:


  Chinook is extremely docile in handling, yet extremely maneuverable when light. Autorotation is of the thistledown type, rotor inertia is massive and the beggar wont come down fast even if you want it too. Engine off landing is merely a continuous flare to a running landing on the rear wheels which requires quite a lot of runway. I dont know if the military use other techniques.


So in short, the Chinook config has pros and cons. The two rotors' wakes intermingle with a reduced power efficiency in forward flight. From same thread as above:


  Due to the dynamics the Chinook develops maximum translational lift in sideways flight to the left, hence the antics of the logging machines plugung sideways on the end of theit long cables - gives them greatly increased lift capacity.


So yes the twin counter rotating rotor does not spill tail rotor power during the hover and has a large payload range. It has a longer but narrower footprint than a similar MTOW single rotor. But it is not universally more power frugal than the single rotor config.





Co-axial. Picture above from this question.

The co-axial setup main drawback is its complexity. Counter rotating shafts, one in the other. One rotor quite high over the other one to allow relative flapping. Super complicated control actuation.

Power requirements: the coaxial configuration has power requirements according to this answer. 


All in all, the counter rotating setup is simpler than the coaxial setup, which does have the advantage of a very small footprint. But the single rotor set-up has proven to be the configuration with the best design balance.