I have very limited strop experience/expertise, but from what I've seen, the rough side can load up more compound than the smooth side. As far as the thickness, if you're mounting it to a hard backing, then thinner leather will deform less and be a "harder" strop, and thicker leather will give more and be a "softer" strop. I would imagine that if you're using the strop like a barber, just pulling the leather tight between two points, then it would be sort of the reverse, where the thinner leather would give more and the thicker would give less.