My friend says that the buoyant force on an elephant..?

that sounds like you 2 must be smoking pot....anyway onto buoyancy. Archimedes' principle states that an object fully or partly immersed in a liquid is buoyed upward by a force equal to the weight of the liquid displaced by that object. From this principle, he concluded that a floating object displaces an amount of liquid equal to its own weight. With that being said an elephant will displace more water then a balloon so an elephant is more buoyant.