Voltage and current don't matter.
Turns and wire size are open variables. You can only put on as much copper as the assembly will hold, period. And you can only dissipate so much heat as the assembly will allow (given that you can fill the winding with conductive potting, and heatsink it, or add cooling tubes and water flow if you're desperate).
Thus, the amount of magnetic field intensity you can obtain, from a given quantity of copper, requires a fixed power input. The copper's resistance is the conversion factor between power (volts * amps, heat dissipated) and magnetic field intensity (amps * turns / magnetic path length), which is also an energy figure (energy density is B^2 / (2*mu)).
It's not truly constant because it depends on available power, dissipation capacity, geometry and pole pieces, but those are only ratios that tweak the total. But the copper, you can't do any better with anything else.
If battery operation is required, I would seriously consider using as many efficiency enhancements as possible:
1. PWM DC, obviously. Preferably filtered, to reduce core heating.
2. Relatively low current density, to reduce power dissipation. Requires a physically larger winding (more copper).
3. Pole pieces. An iron core goes through the winding and shorts out much of the magnetic path length, increasing the field intensity (in the remaining gap) proportionally.
4. Permanent bias. Magnets are added to the core to provide a background field which is the average level required by the application.
If you need an always-on field, then you can use all permanent magnets, with only very little electrical input required for trimming it around the desired level.
If you need to go from zero to (peak) approximately equal amounts of the time, then use magnets for (peak)/2 bias, and electrical drive to +/-(peak)/2, thus achieving the 0 to (peak) range with half the electrical requirement.
If the duty cycle is uneven, bias accordingly. If the magnet is off most of the time, use less bias (or none, since it will be inconvenient to use very tiny magnets at some point), and pulse it on to enable. If it's on most of the time, use more bias, and pulse it to disable (opposing the permanent field with the electromagnet).
Tim