Home project: 120VAC or 240VAC? Help plz.

Doing a home project and I am trying to figure out which voltage to use.  I know here in America that utility companies charge by KWH.  I am trying to figure out which heating element would be best for time and cost less.  120VAC 3000 watts or 240 volts 7500 watts?  I do know the higher the wattage the faster the heating process.  Amperage is another conern.  I thought when voltage goes up the amperage goes down?  If you do the math the 120 volts heating element it will be pulling 25A.  When you do the math for the 240 volts heating element you get 31.25A.  Shouldn't the amperage would be lower for the 7500 watts heating element be lower than the 3000 heating element?

When and why would people want to up there voltage from 120vac to 240vac?

True if the power dissipation is the same, but you have upped the power for the 240V element. For a 3000W element in both cases, you half the current at 240V.
The limit is probably going to be on the wiring if it is already in place, it would have a rating similar to that used on an electric stove, for example.
240V has the advantage of half the current for the same power pulled, so lighter wiring, or twice the power for the wiring rated for the 120V application.
The split phase system has more to do with the network distribution of power from the providers end, and power loss in cables,
Cheers,
Richard