Air layering is usually used with plants that are reluctant to root and cuttings from which usually dehydrate or starve to death before roots have formed. Occasionally it's very easy too (I have a rosemary bush which has some branches that sagged to the ground and 'air layered' themselves on their own).

With an air layer you can keep all the leaves and take a cutting larger than would survive a cut-n-root approach, and the cutting will continue to grow while it roots. That's probably the main benefit in easy to root plants.

I know a guy who uses peat plugs to make his cuttings.
He cuts the expanded plugs half way through.
Then he scratches up a branch on his plant and puts rooting hormone on that area.
Slip the peat plug over the area with the rooting powder and tie it closed.
Wrap the whole plug with plastic wrap and wait for roots to grow through the plug.
Cut off the rooted branch under the roots and pot it up.
Seems to work pretty good from what I've seen.
I don't know how long it took for roots to grow.