Most efficient compressor---
use logic to find the answer.-
a simple piston in a sealed sleeve.
move the piston - ALL the air is compressed ahead of the moving piston.move it slowly or rapidly -makes no difference if you disregard heat buildup.
This is --effectively--a positive displacement compressor.
for moving air -NOT just compressing air - an entirely different set of requirements -
A supercharger --can be made from many types of devices --including the piston in a sleeve. The types of superchargers are varied and depending on the rpm range and speed the flow / efficiency etc., varies dramatically..
Air movers for buildings are another catagory - lots of air is moved at a very slight increase in pressure
with the exception of the sealed chamber and piston , all other types have losses due to many reasons
The logic is this :
air will always take the path of least resistance
It may simply sneak around the impellors -or cavitate -
The reason most cars still use piston engines is that this is the most efficient method of controlling pressures .