If you truly mean "composite", there is no difference. A longbow can be composite if it's constructed of multiple layers of wood and fiberglass or it can be a "self" bow meaning constructed out a single piece of wood. If you really mean a "compound" bow, There's a big difference. Compound bows use mechanically rotating cams to provide the energy to propel the arrow, whereas a longbow is a stick and a string. Bending the long limbs provide the energy.