Not an expert, but I am a bit of a Physics buff.

Higher displacement would mean it's able to move more refrigerant (higher cooling performance) when all else are equal... particularly the compressor shaft RPM. Hence, moving 120cc of refrigerant will put a bit more load on the engine than say a compressor pushing just 85cc.

As far as compressor goes, cooling performance is a function of how much refrigerant it can move at a given time. Other factors come into play (ie. evaporator and/or condenser size, engine displacement, operational RPM range, passenger cabin volume, etc.) when designing which compressor is best for a particular vehicle. Manufacturers typically wants the best compromise of having good cooling performance while still being fuel-efficient.