High voltage power lines: helicoptor versus birds
The amount of current needed to bring a suspended object to the same potential as a conductor is proportional to the capacitance between the object and earth.  Since the helicopter is a big object made of metal, and the potential of the line is very high, lots of charge has to flow in order to bring it to line potential.  A bird, being much smaller and much less conductive has a much lower capacitance to earth and therefore much less current is needed to bring it to line potential. My guess is that for very high voltage lines even the bird will feel a zap.