The degree of efficiency of a 2-stage compressor vs. single stage depends heavily on the stroke as well as the piston diameter of the high side with respect to the low pressure side.
But, to really understand efficiency, we have to look at power input vs desired output. If the desired output is pressure, then the single stage can't compete as the pressures it can reliably achieve are limited by its design. If it's volume, however, the 2-stage is simply overwhelmed by elementary physics alone, given equivalent RPM, stroke and low-side piston diameters. This presumes that both have the required power input to drive each at equivalent RPMs and maintain a constant temperature, which we know will never happen - 2-stage compressors are always pushing more heat, which will lessen their thermodynamic efficiency to some degree.
In terms of less internal stress, that is also heavily dependent. It's probably not going to be less stress, otherwise the high-side wrist pin wouldn't be the first place to look for a 2-stage compressor knock. Also, the valve bumpers on 2-stage compressors take significantly more abuse on the high-side than single stage compressors at any point, as do the rest of the parts inline with air delivery to the receiver.
All that being said, I still prefer to use a 2-stage compressor, simply because if nothing else, I love the thermodynamic complications it entails.