Does a full freezer run more efficiently?

A full freezer retains cold better than an empty one. When you open the door, the mass of frozen food will help keep in the cold, and the unit won't have to work as hard to cool empty space. But don't jam pack the freezer either; you need air to circulate.

Does an empty freezer run more than a full freezer?

Although a full freezer runs more efficiently than an empty freezer, overfilling a freezer does not provide the ultimate in savings. Instead, an overfull freezer decreases efficiency because of the inability of the sensor to read the temperature properly.