Both have distinct uses and both represent different aesthetics. Chosing a rope can be an intuitive process where the tactile feel is natural and the appearance important. Regardless of your choice always make sure the rope is strong enough for the task. Natural rope can be made from cotton, flax, silk, hemp, manilla, coir, papyrus, and a plethora of uncommon plants and barks. Most of these ropes have a coarse texture and are stiff to bend.
Natural rope can leave abrasions on the skin and 'hair' splinters.
Burns are easy to create with hemp and manilla rope. Let alone a full medical examining table and stirups. Natural rope's disadvantages are that it swells when wet. More so, it has a realativly weak load ratio for it's diameter. Natural rope has a nostalgia many people are attracted to.