The balloon filled with air will register the greater weight.
Work Step by Step
It may seem that the two items will register equal weights, because the buoyant force on the inflated balloon seems to be exactly compensated by the weight of the air inside the balloon. However, the air inside a stretched balloon is at a higher pressure than the outside air (see question 78). The balloon's stretched material, in trying to return to its original size, provides an inward pressure. The gas pressure inside must overcome this pressure plus the outside air pressure. (Additional proof: stick a pin into the balloon. If the inside and outside pressures were equal, there would be no tendency for air to flow to equalize pressures, and it would be an unremarkable event.) The density of the air inside the balloon will be greater than that of the air outside. The weight of the the air inside exceeds the weight of an equal volume of displaced outside air, which means it exceeds the buoyant force. The scale will show a greater weight for the inflated balloon.