Expansion or compression -- which is more energy efficient?

[T C]

where A is the area of the piston, and the differential displacement of the piston is ds=dV/A. This is the work that is used in the first law of thermodynamics, and is equal to the decrease in internal energy of the gas (for adiabatic change). It is what you are calling the total "energy consumption."

No. The gas works as it expands and the piston works by pulling atmospheric pressure outwards. The work done by the piston against the atmospheric pressure is positive here while the work done by the gas is negative. It has to be deducted from the work done by the done against the atmospheric pressure.

here is no energy consumption involved in advancing the piston for the case of a massless, frictionless piston. The work done by the gas on one side of the piston is equal in magnitude to the work done on the other side of the piston by the atmosphere and the pulling force

How can you say so? The piston is working against the atmospheric pressure and the gas inside is working on the piston. So get the net energy expenditure, we have to deduct the work done by the gas inside from the work done by the piston by working against atmospheric pressure.