Warm and Natural is the only batting I know of that has a right side and wrong side. With other battings, there is typically no need to be concerned about which side is up.
Warm and Natural is needlepunched through scrim, which makes it extremely stable, with quilting lines at a max of 10" apart. Vintage cotton batting (such as Mountain Mist) is the type that is not needlepunched or bonded, requiring quilting lines no more than 2" apart.
In-between those two extremes are cotton battings that are bonded (for example, Hobbs 80/20) and cotton battings that are needlepunched but not through scrim (Quilter's Dream cotton). The distance between quilting lines for these battings also falls in-between the two extremes.