Here is the answer to your question, based on some science and some assumptions, with the Hobie bait tank pump.
12V battery directly connected uses 16.5 watts of power (and way too much water flow).
12V battery and the resistor uses 6.3 watts of power.
12V battery and the step down module uses 5.6 watts of power.
12V battery and the PWM uses 4.3 watts of power.
6V battery directly connected uses 3.2 watts of power.
Watts is what gets the work done and what the battery needs to supply, so in simple terms, ignoring a few messy details, the 6V battery is the most efficient and will last the longest. That's what I use on my Hobie.
Here is a photo of the elusive PWM. I put it together many years ago for my 12V (non-Hobie) kayak and its still works well.
Enough science for now, my head hurts, lets go
