False.

Your electrical cost will not go down.

The equipment still uses the same amount of power (rated in watts).  You are billed by kwh (# of watts / 1000 * cost per kwh = cost per hour to run equipment).

If you deliver 1100 watts on 110v power, that's 10A.

If you deliver 1100 watts on 220v power, that's 5A.

Still the same 1100 watts.