I have a bad habit of referring to the right and wrong sides of the cloth. I should say "face" and "reverse", or better yet, "public side" and "private side". (And as for where I should put the punctuation marks, inside or outside the quotes, I give up! When I do it right, it looks funny.) Sometimes we weave cloth reverse side up because the shaft lifting combinations are lighter. And sometimes we weave cloth face up and decide we actually like the reverse side better. And sometimes there really is a right side (fewer long floats for upholstery, for instance), and the reverse side is more attractive even though it is not technically "right."
In my most recent batch of crepe samples, I have one that looks much prettier on the reverse side. Here it is before and after wet finishing. As usual, click to enlarge. It is composed of stripes of 8-end crepe, 8-end granite (a satin derivative) and 2/2 twill selvedges.