How is auto-rotation different in coaxial rotor helicopters?
There's one major difference between a coaxial helicopter and a conventional single main rotor -- single tail rotor helicopter during autorotation: yaw control.

A conventional helicopter has a main rotor which produces a torque. The tail rotor thrust, applied at the end of the tail boom, provides a counter-acting "anti-torque" to keep the helicopter pointing when the pilot wants it.  As the pilot, when I change the collective pitch of the main rotor, to go into a climb or a descent, the torque required to drive the main rotor goes up or down, and the pilot counters by raising or lowering the tail rotor collective to change the tail rotor thrust to match.  Additionally, if I want to yaw the nose to the left or right, I can use the pedals to raise or lower the tail rotor thrust in order to temporarily upset the balance between the main and tail rotor torques and steer the aircraft.

Now, consider how yaw control works for a coaxial helicopter.  The torque of the upper rotor is now counter-balanced by the torque of the lower rotor.  To yaw the helicopter, the pedal inputs are set up to upset the balance of torques by raising the torque on one rotor (by increasing the collective) and lowering it on the other (decreasing collective), while maintaining the same thrust.

Now, when I increase my rate of descent to autorotation, the engines are no longer providing torque to drive the main rotor--the rotor is being driven by the relative wind.  In a conventional helicopter, the tail rotor is still being driven by torque transmitted from the main rotor through the drive shafts--so while there's no main rotor torque to balance, I can still use the pedals to change the tail rotor thrust and control my yaw.  However, in a coaxial helicopter, when the  torque on the rotors is low, differential collective does not have very much control authority: depending on the collective setting, pedal inputs can have a weak effect, no effect, or most surprisingly, a negative effect!  To counter-act this, most coaxial helicopters have very large vertical fins to provide good low-speed directional stability and many have rudders to augment control.

For instance, here's a picture showing the empennage of the Kamov Ka-25 (from aviastar.org).
 

More modern machines also have control systems that reverse the effect of pedal inputs on differential collective at the very low collective stick settings where control reversal can occur.  Flight manuals for coaxial helicopters advise against reducing forward speed too quickly during autorotation, since the directional stability is provided primarily by the body and tail.