To attempt a generalized version of sibling comment from radford-neal, the energy that goes specifically into changing the position of the payload is the same,

To attempt a generalized version of sibling comment from radford-neal, the energy that goes specifically into changing the position of the payload is the same, but how much of the total energy spent goes into that, depends on the method. For the rocket energy goes into so many things other than lifting the payload: kinetic energy of the exhaust, high temperature, sound, and - most importantly - lifting the fuel itself, quickly. Or to think another way think of all the challenges with human powered helicopter where the record is reaching 3.3 meters in 64 second flight, whereas any moderately physically fit person can climb the same height on the rope much faster and hang out there indefinitely, because they did not have to lift the weight of the helicopter and send the big masses of swooshing air down from the blades just to combat the force of gravity.