The debate about Slow running Air-Compressors or high speed Air-Compressors is an ongoing discussion.

Slow running mechanical systems have traditionally more favourable running conditions because the mechanical system is less loaded and therefor more robust and has a longer lifetime.  Typical examples are the industrial piston compressors which run very slow around 400-1000 rpm.  Due to their low rpm, the lifetime of these compressors can go up to more than 40 years.
An Oil-free screw compressor will run tipspeeds up to 100m/s or 3000-30000rpm of the rotors depending on the size or  diameter of the rotor.  In Oil-free screw compressors, various manufacturers run at different rotational speeds.


And what about the high speed compressors ?  

When running a compressor faster, the mechanical system becomes more stressed.   The benefit of running faster however is that the compressor capacity  increases with increasing the rotational speed.  That results in more output flow for the same cost or same output flow for lesser cost.  Of course, mostly the reduction of cost is to the benefit of the manufacturer and not the user.

What about the energy efficiency of slow running compressors ?

Slow running compressors often have a better energy efficiency due to the better volumetric efficiency and less mechanical losses.  Examples are slow running piston compressors and Oil-free screw compressors with larger slow running air-ends.

What about centrifgugal compressors, they are high speed running machines. ?

Centrifugal compressors are dynamic compressors and not volumetric compressors.  They operate on different principles.  For dynamic compressors, it is crucial to determine the max operating speed and reducing the mechanical losses by use of low friction bearings such as magnetic bearings.