What is the difference between air layering and cuttings? When would one be better than the other? 

I air layered a branch on a Japanese cherry. It was down a steep hill pretty far from the house, so I forgot to go check on it fairly often; in the drought we just had the birds came and pecked holes in the plastic and tin foil more than once. I tried renewing the water inside the peat moss, but the branch was without several times.

It seems that cutting a strip of bark off is no different than cutting the entire branch off. If I take a cutting I can stick it in cutting medium on the back porch and care would be a lot easier. Advantages?

Airlayers is for thick brances, cutting for thin twigs.

The disadvantage of cutting is that they take 10 years or more to be the same size as a good airlayer.