Yes, that is true in theory and in my experience also. One thing to consider is the formula for power: current squared times the resistance. Look at it like this -- the resistance of supply wiring and motor windings is fixed -- a function of the cross sectional area, length and material of the conductors -- fixed resistance. If you change a machine from 110V to 220V, the current is essentially cut in half. And halving the current will reduce the lost power/heat to only 25% of what it was at 110V -- more power available to the motor and cooler operation to boot....
That said, if you are using a VFD, such as the Delta Electronics S1 box that is on the back of most modern lathes, along with a three-phase motor, there is a bunch of other factors... Regardless, it is still good practice to use 220V wherever practical.
BTW, love your videos and hope to perhaps get to meet you one day, Robo!
Ely