I love my flax linen (the REAL deal) strop, and always use it before I hit the horse butt. I also have a cotton "linen" strop which I used prior to getting the linen strop, and both work just fine for me. But the flax linen has a tactile character that I prefer that's just not there with the cotton fabric.
BTW: I use my fabric strops "nekkid". I think that I'll leave them that way, and will get other strops for pasting.