I have hanging strops and a paddle strop, and prefer the hangers by a long shot. When I use the paddle strop, I often rest the round end of the handle on something that allows the paddle to rotate with my stropping stroke, as the hanger is free to do. That might be a peculiarity of my own stropping, but there it is.

I agree with Birnando that the SRD modular paddle is a great tool. I use it for travel and for pasted stropping. For daily, at-home stropping, though, I prefer the hangers.