A scroll compresssor/expander is a (kinda) positive-displacement machine, albeit a leaky one. A turbine is a turbomachine.
You've given us NO indication of the scale of the equipment or what it's for or how it's going to be used. "more information = better answers". That in mind ...
Positive-displacement "stuff" (compressors, engines, expanders, etc) tends to be better at smaller sizes. Turbomachinery tends to be better at larger sizes. A lot of this has to do with a fluid-dynamic concept called the "Reynolds number". This is why your household refrigerator or air-conditioning unit compressor is a positive-displacement apparatus whereas the electrical generating station that supplies electricity to your city is a turbomachine.
Positive-displacement "stuff" (compressors, engines, expanders, etc) tends to work decently over a fairly wide range of operating speed and load without the efficiency becoming atrocious. Turbomachinery tends to like staying close to its design power and speed, and the efficiency drops into the toilet at low operating speed. This - in addition to the Reynolds-number-related scaling effects - is why the engine in your car (which probably functions adequately from 800rpm idle to 6000 rpm full power) is a positive-displacement device, and the engine in a transcontinental airliner (idle speed is probably half-ish maximum rated load) is a turbomachine.