I am assuming that by cooling you are referring as to which Engine cooling systems are better in particular scenarios...
Oil-cooled: Traditional Oil-cooled engines are most commonly found in passenger commuter motorcycles which are usually anywhere between 50cc to 500cc (some sophisticated models have liquid cooled engines as well). The system uses the already present engine oil as a source for cooling the engine. It is generally supported by radiator-type fins (which one can see attached to such engines, typically on a motorcycle)
Liquid-cooling: Most common on passenger cars and motorcycles as well. Include a separate coolant as the basis to reduce engine temperature via a series of Radiator assembly components - grille, pipes, fins and majorly a rotating electric fan.
Uses of one over another:
A1. Oil-cooled engines have Compact design, since there is no requirement of additional components like radiator-fan assemblies in liquid cooled ones.
A2. Oil having a higher boiling point, can fight against high temperature evaporation as opposed to coolant (or water cooling the engine in adverse times).
A3. Oil doesn't cause rust and acts as an insulator against electric sparks or something.
A4. Traditionally, oil and air-cooling were preferred in extreme applications like military where there is a possibility of damage to liquid-cooling system components.
B1. Liquid-cooling is preferred specially for efficiency since liquids work better than air for heat exchange as per physics.
B2. Works favorably better for high performance and race-oriented cars.
B3. Oil may degrade and leave residues overtime and relying only on one source of something is disadvantageous as opposed to having dedicated cooling systems.
B4. Finally, oil has chances of lighting up if spillage or leakage occurs due to the hot engine temperature and water is readily available in the event your coolant wears/leaks off, etc.