First off, my answer is short because I think this is far more of an engineering or aviation SE question than a physics one.
To directly answer your question,
any coaxial rotor setup is inherently less efficient than the individual blade arrangement of the Chinook helicopter, for example, that you cite in your post. The aerodynamic efficiency of the coaxial arrangement compares badly, overall, in many ways, than the Chinook example.
To give one example of why this is so, is due to the fact that the upper rotor has ( I am very aware that this might be obvious), more of an predominant role than the lower rotor.
Ignoring the complexity of the coaxial system, (which is definetely more engineering more than physics ), in fluid dynamical terms, there are undesirable aerodynamic interactions between the rotors.
The upper rotor produces a greater amount of downwash velocity on the swept area covered by the lower rotor, which is again not difficult to justify intuitively, than either blade would in the Chinook example.
An obvious workaround for this inefficiency is to increase the spacing between the blades, but this adaption, although it has the effect of increasing the thrust coefficient of the top rotor, results in the total thrust coefficient of the entire system becoming slightly reduced, compared to a single blade system.
So, if that is just one disadvantage, why where they built in the first place?
Coaxial helicopters were designed, in part, to obviate the need for a tail rotor, which has advantages in both tree covered terrain and for military use (both in low altitude flying patterns).
However, from personal experience (at an airshow), I have to say that these coaxial helicopters are particularly loud, conpared to a single main rotor and a smaller tail rotor, which reduces their miilitary advantage.