I cut most of my bindings on the bias, whether it will go on curves or straight, so it doesn't matter which way is the length or the width. However, if I do choose to cut a straight binding, or a border or sashing for that matter, I prefer to cut it on the lengthwise of the fabric. The lengthwise has very little "stretch" compared to the widthwise of the fabric. This is also how you tell the difference when you don't have the selvedge to tell you length or width. Cut long lengthwise pieces first before cutting widthwise pieces. One has to measure carefully as there is less "forgiveness" when the fabric has so little stretch or cut the piece longer than needed; sew with an even-feed foot or sew the pieces together carefully.
Good Luck, Sonia K.