Power consumed (=$) will not change. Power = Voltage x Amperage. Switching between 110 and 220 volts will double the voltage and half the current.
Every time electricity passes through a wire there is a voltage drop due to the resistance of the wire. Voltage Drop = Amperage x Resistance. Switching between 110 and 220 will halve the current and therefore decrease the voltage drop. Additionally, 220 usually uses larger wire diameter (lower wire gauge) which decreases the resistance. Voltage Drop decreases the voltage that reaches the load (motor) which can cause decreased performance and if sufficient drop can damage the motor.
(Note: for simplicity I am using DC equations not the AC ones)
-- Jesse, Saint Louis, Missouri
