re: Aerodynamics of a Cyclogyro (most obvious advantage)
Vertical takeoff and landing. Forward & backward flight. Very high forward speed.
A cyclogyro has no speed limit in horizontal flight. In contrast a helicoper's speed is limited by the fact that one rotor is rotating forward while the other is rotating backward. This places a limit on forward speed. Not true with a cyclogyro.
A cyclogyro could possibly be a vertical takeoff supersonic aircraft.
And it's neat-o.