I might be completely misunderstanding this but I'm pretty sure there is a MASSIVE amp draw difference between these two scenarios.
Thumb smashed on my Galaxy Note 4
Yes there is, but those amp and voltage numbers are what the regulator puts out, not the battery

. Remember, battery voltage is set at what it is at its current state of charge. Fully charged it will be close to 4.2V, when the
mod decides to stop working due to low battery volts it's around 3.3V.
Here is
the Steam Engine battery drain calculator. This is a much easier tool to demonstrate with than getting into the math calcs.
Have a look at "Atomizer - what hits your topper (atty)" and compare it to "Battery drain - what taxes your battery". When I open that page it defaults to 'Regulated VW', 1.9 ohms, 100 watts, 'Battery voltage = 6V (a dual battery mod with almost depleted batts)'. Battery drain amps is 18.52A from each, battery voltage is 3V from each and wattage drawn from the two
batteries is 111.11 watts because of regulator inefficiency loss. Atty voltage is what the regulator puts out in that scenario, 13.78V, 7.25 amps and watts are 100 as set on the mod.
Change the resistance to 0.1 ohms and the numbers for "Battery drain - what taxes your batteries" are the same, but the atty sees 3.16V and 31.62A.
There will be some difference in battery drain that the calculator doesn't show because "APV efficiency (the regulator)" will be different for different voltage outputs, but that is typically +- a few percent so not really significant.