Oil cooled versus water cooled 4 cycle engine?

Water

Actually, it depends on the application. Water cooled is more complex which means typically more expencive. But water (W/antifreeze) transfers heat faster so it maintains a constant temperature better. All new purpose built motors have the use factored into the cooling requirements. so unless you live in an extreme climate either should be fine.
---I live near PHX AZ and road my old air cooled suzuki last week with the outside temp near 118. No problem for the bike but I wilted.

Absolutely water cooled, you don't want to depend on the wind to cool your oil, the same oil that is lubricating the cylinder walls. Once that oil gets hot enough it breaks down and then you are still depending on that same oil to lube the cylinder walls. The main resaon for a liquid cooled bike is to last longer and get more milage out of it and this is why. If you are not depending on the oil to do 2 jobs, it can do its original intended job a whole lot better and that is keeping the cylinder wall cool and clean from scratches. In my opinion liquid cooled all the way.

You can extract more power from a water cooled engine . thats why all performance dirt bikes are water cooled.

You can extract more power from a water cooled engine . thats why all performance 2 stroke dirt bikes are water cooled.