I have both paddle and hanging strops. Since I don't really like the fact that the paddle strops don't give at all, and I manage to dull my razors regularly on a hanging strop, - it seems I'll never learn that! -, I found a third way of stropping that works just perfectly for me. I have a very long vanity cabinet with only one sink, so lots of empty space next to the sink. There, right at the front edge of the cabinet I put my hanging strop, and get the best ever results. No dulling any more, no hanging through, no cupping! It's not the same as having a paddle strop, because the second medium, leather, felt, fabric, etc., depending on which side I use, "cushions" the active side of the strop just a tad. A hanging strop doesn't necessarily need to be hanging just because they call it "hanging". :-)
Hope this will help someone else getting better shaves!