My wife and I eat the greens from our sweet potatoes in salads, stir fry, and in blender smoothies. (Google "sweet potato greens recipes")
Our rabbits love the leaves and stems. As do all the deer in the area.
This year we have added a row of Japanese sweet potatoes. We planted a couple of the potatoes in pots, then cut the sprouts (slips) off and planted those. The leaves are a darker green than the regular sweet potatoes we plant, and taste better raw.