How does flying a helicopter compare with flying a fixed wing plane?
Controlling a helicopter is trickier than controlling a fixed wing aeroplane, because:


a helicopter can hover, in which case it is unstable.
the helicopter rotor is horizontal,
the rotor has long blades, applying a lot of torque to the fuselage.



                
            


The hover. in a conventional helicopter with a single rotor on top, the hover is an unstable situation requiring constant correcting inputs with the cyclic stick, as shown in the above clip. The guest pilot on the left seat has a successful go at controlling the cyclic stick (the stick at the centre), while the impressively capable right seat pilot controls the pedals and the collective stick. The helicopter wants to fall away to the sides and forwards/aft all the time, from disturbances caused by the wake interference with the ground, wind etc. Random accelerations need to be corrected by providing control corrections, based on what the pilot sees in relation with the environment. Peripheral vision is pretty crucial in this, since it rapidly and accurately picks up movements. Four degrees-of-freedom need to be actively controlled: pitch, roll, yaw, vertical speed.

That is all to hover at constant altitude. Now hover and climb: 


increase collective (more eying power), which results in more torque;
so compensate with the pedal input for the tail rotor, which increases sideways thrust;
which must be compensated by lateral cyclic. Three control inputs for one degree-of-freedom!






Horizontal rotor. Once the helicopter picks up speed, its vertical and horizontal stabiliser keep the nose more or less aligned into the airflow - more at higher speed, but the neutral angle also changes with speed. The picture above is also shown in this answer, and depicts what happens with relative blade speed in forward flight. The blade going forward creates more lift than the blade going aft (which is compensated by increasing the Angle of Attack (AoA) of the retreating blade), but there is an area of reverse flow to the side of the rotor axis which results in a sideways tilt of the rotor. Which must be compensated by a cyclic stick left input, more stick at higher speed.
Rotor torque. Installed engine power equates to torque applied to the rotor, times the rotor rotational speed. A propeller is smaller than a rotor and rotates faster: the propeller requires less torque application for a given engine power setting, and the ailerons at the end of the long fixed wings can easily compensate for that. The helicopter rotor requires a lot of torque, which requires a tail rotor to compensate. The faster the helicopter flies, the more torque, the more force required from the tail rotor - which thrusts sideways, creating a drift in the flight path, which must be trimmed by the lateral stick. Even with a vertical stabiliser, tail rotor thrust is a function of airspeed.


Humans can learn to control helicopters of course, but there is a lot more to it than controlling a fixed wing aeroplane. Our brains rely on inner ear and visual inputs for detecting accelerations. More brain stimulation by input detection via multiple channels, results in more precise control. Plus experience of course.But take away an input, like the peripheral vision when flying in reduced visibility, and the control of a helicopter becomes much harder.

In larger helicopters such as S76s, pilot control is helped by a Stability Augmentation System (SAS), an Inner Loop system with no feedback on the flight controls; and an Automatic Flight Control System (AFCS) which changes the trim point of the flight controls as a function of flight path and target point. But these systems are not flight critical: if they fail, the pilot must take over, and must be able to fully control the helicopter by manual input. From visual and inner ear cues, and this always remains harder than in the auto stabilising fixed wing.

Fixed wing aeroplanes can and must be designed to be aerodynamically stable. Helicopters cannot.