The first wave of electric-vehicle batteries is reaching the end of the road, and China and the West are taking very different paths on what to do with them. An electric car battery wears out after about a decade. It is too weak by then to drive far, but still holds plenty of charge for lighter work, and that leftover life can be used two ways: The battery can be kept whole to store electricity, or shredded so the lithium, nickel, and cobalt inside can be recycled for new ones.