What is the difference between free fall on earth and moon?

Even though the mass of earth is greater than of moon one might get tricked into thinking that acceleration due to gravity in earth is greater on earth than on moon so obviously object falls faster under the effect of gravity on earth compared to on moon. This would be true if earth had no atmosphere! Because of atmosphere air resistance after certain time of fall, balances the downward acting gravitational force. And due to this balance an object attains a constant velocity which is also called terminal velocity. From this point object cannot accelerate any more. But on moon there is no air resistance and hence no resisting force to reduce the acceleration. 

Hence, object on moon falls with higher acceleration and not on earth.