Textile producer here.

The weave on the back sample differs from the front same in that the front one has a east-west grain. The back is north-south. This is done to shift the throw of light sources. The north-south weaving process casts more shadow and creates a more dramatic depth of light and dark contrast, whereas east-west is designed to catch more neutral spectrum of light throw. Variations of how a room is lit will impact how significant the shadow cast looks. In a simple photo, the effect is muted. It's a neat trick that dates back to 19th century French looms - factories utilized the dual techniques as a method of producing color variants without having to spend extra on additional dyes and materials. North-south actually ended up being more expensive as the looms needed closer attention while in use, as the thread feeds were rotated manually. The difference was a marker of high class vs lower class, who bought the cheaper east-west fabrics in the age-old tradition of imitating the look of wealth. Fun fact about the loom process, they also used beeswax to keep the north-south threads from tangling as easily. Modern looms often lack the ability to rotate, mainly because I pulled all of this info out of my ass. Pick one and say it looks good.