translate it directly into English, It will be that girl with long hair that girl has long hair 留著 will have same meaning as "have" and "with" have、with = 有著 but 留著 will be more like have her hair growing without cutting it so basically 留著 = have = with = 有著 but 留著 give you an image, the hair is left there growing ~ if you talk to a Chinese, 那个女人留着长发. there is literally no difference between them (留著、有著) (那个女人有着长发) unless you wanna emphasis the image but that will depend on your whole conversation

那 个 女人 留着 长 发 = that girl keeps long hair