Timbeau,
The definite answer is... it depends.
The temperature difference you are concered with is the difference between evaporating and condensing temperatures. Compressors are split up into application ranges, which means the compressor is optimized for a certain combination of evap/cond. temps.
High Temp/Air Conditioning 45/130
Medium Temp: 20/120
Low Temp 0/105
Ultra Low Temp -20/105
Cyrogenics Lower than everything above
These are not hard and fast rules, and there are ranges in between. There compressors that are "extended medium temp."
What is happening is that for every evaporating and condensing temp there is a corresponding saturation pressure. The difference in pressure from evaporating to condensing is called the compression ratio. This is one of the major factors in compressor selection. The compressor required to move 1 ton in an air conditioner not only has a smaller motor, but the compression mechanism is built totally different than one required to move 1 ton in a freezer.
The freezer has a much higher compression ratio.
The refrigerant selction also is important. A scroll compressor using R404a can accomodate slightly higher compression ratios than the equivalent compressor using R22.
Operating a compressor outside it's application range will kill the compressor. It sounds paradoxical, but one of the biggest compressor killers in low temp applications is compressor overheating.
Low temperature applications also cost more per BTU than high temp, because the compressor is physically larger, plus there are devices required to keep the compressor and its oil from over heating. Liquid injection and oil coolers are some examples.
All of this applies to single stage systems, which means all of the compression is done in one stroke. Multi stage systems are often used in ultra low or cryogenics, because of the high compression ratios. Basically the total compression ratio is divided up in different cylinders or compressors. Another way of doing this is a cascade sytem.
But this is getting way too long, and cryogenics is out of my knowledge base.
Good Luck