I'm going to step out on a limb here, but my understanding is that the resistance DOES play a factor because it's going to determine what current is required by the coil.
Ohm's Law - Volts = Current * Resistance
Watt's Law - Watts = Volts^2 / Resistance (or Watts = Current^2 * Resistance)
Resistance is the constant, whereas either volts or watts gets set on a regulated device, or the remaining charge on the battery determines the available volts for a mech.
On a regulated device, if I have a 1ohm coil and I throw 30W on that, the device will apply 5.5V (even though the charge of the battery may only be 4.2V max - buck/boost circuity will push the higher voltage.) Therefore, I'd be running 5.5A through the coil. If I now do the same thing with a 2ohm coil, I'd be applying 7.8V across the coil, but only drawing 3.9A through the coil. Drawing lower Amps should mean that the battery would last a little longer.
On regulated mods, you set either Watts or Volts, and because the resistance is a constant, the opposite (Volts or Watts) is derived accordingly. Mech mods don't have the buck/boost to change the voltage applied to the coil, so the power output effectively changes as the charge on the battery drains. In order to "generate" higher wattage, the resistance of the coils has to decrease, but that can only decrease to not overdrive the discharge current of the battery. If I have a freshly charged battery (presume 4.2V) and a 0.5 ohm coil, I'm going to yield just over 35W (4.2*4.2/0.5), and I need a battery that can continuously deliver 8.4A current (4.2/0.5) As the charge on the battery decreases, let's say 3.8V, you'll be achieving about 29W, but you still need to deliver 7.6A from the battery.