Both fluids are utilized, and also with a third variant 'gas over oil' combined to give an assured oil pressure.
Different solutions are used, depending on a number of factors. One important factor is of course the cheapest commercial solution available ('common practice for size, process fluid (not actuator fluid), pressure class, valve type, size, speed of closure, and branch/application)
No firm rules can in my mind be set down, but you will find firm opinions if you start with an exact application and process type.
Some general tendencies (not firm rules) can be put down:
Smaller valves, air used elswhere -> air
Larger valves, hydraulic used elsewhere -> hydraulic
Faster movement -> air or fallweight closed hydraulic cylinders if larger valvetypes.
Slower or controlled movement -> trotteled air or better controlled (perhaps) hydraulic.
Valves on hydraulic operated machines -> hydraulic
Submerged -> hydraulic
Valves remote from electricity or sources for common air or oil hydraulics -> electric, battery backed, or handpumped hydraulics or battery backed electric. More seldom air.