It is not just the heat differential that matters but also the ability to cool. I don't know about engines, but for people, we lose it is said 25 *times* more heat in water than we do in air with the same temperature. That's why hypothermia occurs very fast (minutes) in cold water where we can survive hours in the same temperature air.
The only way to settle that is by looking at the math formulae for the heat exchange with liquids and gasses and plug-in several heat differential values and the correct heat absorption (heat capacity) values and see if the larger heat differential under normal operating temperatures with air will outweigh the higher heat absorption capacity of the coolant.
I'll give another empirical example of water cooling being a LOT more effective than air cooling, with *exactly* the same temperature differential and exactly the same cooling surfaces in both cases. I make home-made yogurt. The milk is boiled, so 212F. It needs to cool off to about 112F before I add the yogurt starter, which dies in hotter milk and does not work well in colder milk. If I leave the container with hot milk to cool in the air on the porch outside, it takes several hours to cool-off in 40F air. It takes just minutes in 40F tap water to cool off. Now, that might not be fair, because I replace the water that warms-up with colder water from the tap, where on a motorbike I would need to air-cool it with a radiator, and if that radiator is small, it won't be as effective as just getting new cold liquid in the system as I do with the milk. But the point of radiators is not just to get the air cooling exchange in a better place where there is more airflow, but to also have a larger cooling surface than the motor would allow. So they increase the heat exchange 3-ways: more cooling surface, better circulation, higher thermal capacity of the liquid.