What is the purpose of having contra-rotating props on an aircraft?
According to my experience, you have two problems with props:


Torque
Exhaust Speed


If you use contra-rotating propellers, you eliminate the torque reaction problem because you now have two contra-rotating propellers each cancelling out the opposite's torque.

Also you increase the speed of air accelerated by the propellers, thus the aircraft’s efficiency at relatively high travelling speeds is increased.

Normally, the propeller can only be operated effectively at low Mach numbers and increasing the RPM above a certain point will only cause the air behind the propeller to compress but not accelerate. Using a second propeller with higher pitch angles can generate high enough airspeed without the problem of compression because the second propeller is rotating inside the airstream generated by the first propeller.

Correction
However, having a different speed and pitch WILL induce a torque effect.