Hanging strops and paddle (or bench) strops serve similar, yet slightly different purposes. With a paddle strop, the stropping surface is flat, just like a razor hone is flat (or at least should be). When you use a paddle strop, you are putting equal pressure on the spine and edge, just as you would when honing. Thus, a paddle strop is good for producing a keen edge on the razor after honing. Abrasive pastes and sprays work well on paddle strops to produce a keen edge. Diamond and cubic boron nitride (CBN) sprays and pastes are often used on paddle strops to produce a keen edge.
With a hanging strop, the stropping medium (cloth or leather) does not remain flat. It deflects as you strop the razor along the surface of the strop. This stropping action, combined with the deflection of the strop, concentrates much of the pressure on the edge of the razor. This action tends to round off and polish the edge of the razor. This makes a keen edge more comfortable. Chromium oxide is often used on a hanging strop to make the edge smoother and more comfortable.
Thus, both paddle strops and hanging strops serve a useful purpose. If you want to optimize your shaving experience, learn how to use both.
Since you continue to nick your hanging leather strop, there must be something wrong in your stropping technique. Keep the spine in contact with the strop at all times. You have to time and flip and the change in stroke direction so that you are always moving towards the spine and away from the edge. Otherwise, you will nick the strop. Go slowly and deliberately until you can master the flip, then try to pick up speed later.
There are some excellent YouTube videos on stropping. Here is a good one by Lynn Abrams.
https://www.youtube.com/watch?v=
