well... trick question.
one will run cheaper than the other, but only very slightly. here's why:
what really matters is not the ballast's voltage, but the ballast's
power factor.
a ballast is an inductive load... so its going to have a low power factor to begin with. your cheaper magnetic ballasts typically have the lowest power factors, while digital ballasts have active power factor correctors built in, which gives them a higher power factor rating. (this is also what makes them 'digital', FYI.)
you could say that the power factor is a measurement of efficiency of the wattage/current demand of an energized device.
however, unfortunately, the power companies bill you for wattage, not amperage. because amperage is inversely proportionate to voltage, however wattage remains the same.
example-
1000w @ 120v = 8.333 amps
1000w @ 240v = 4.166 amps
so why do I save money when i use 240v then, if the wattage never changes?
that, is a rather simple question now that you know what power factor is.
the power factor of a device is dependent on the amperage of the circuit.... the power factor is determined by:
the lower the amperage, the higher the power factor.
a 240v ballast uses less amperage than a 120v ballast, both pulling the same watts, which increases the 240v ballasts power factor... in laymans terms, because its more efficient.
hope i didnt confuse you to bad. power factor is a complex thing to understand, and i tried to keep it as simple as I could.