It seems to me the energy use would be much higher since there isn't a counterweight to offset some of the mass that the linear motor needs to move (the cars and its contents).  All motors convert energy to force.  Unless Newton's laws of motion somehow don't apply anymore, more energy will be necessary to create the force to move the car without the obvious gravity-negating mechanism of the counterweight as gravity is one major force to deal with in all elevators/lifts.