Oh, you beat me to it! I was interested in the same question. ;-)

I have both a paddle strop and hanging strop and get great results with both. My theory is that the hanging strop is more convenient and gives you the ability to 'tune' the taughtness while stropping for people that are really good at it.

For me... I use the paddle strop when I'm honing to finish a blade and the hanging strop for maintenance pre/post.

Very interested to see what others say... Great question!