Short answer not really, any voltage level used will require some type of conversion. Most batteries do not output a constant voltage output anyway, unless connected to a regulated power cable (another conversion process), so get get a battery or other power source with the correct voltage level.
The advantages of using a normal 14.5 VDC camera battery is, the higher voltage and MA provide more power, and 14 VDC an given amperage will provide the required 12 VDC level longer than a battery that only outputs 12 VDC at the same amperage, See Ohm’s law to see how this works.
I have tried running the original Pocket camera with a large 7.2 VDC battery (which was around 9.x VDC fully charged, and it would power up the small Pocket camera if I had an internal battery in it (not a BMD recommended practice when using a 12-VDC upscaling source) the original Pocket camera was combining the two batteries together at the DC-DC power supply, but this was not very good, and only Extended the run time by around 50 percent, not 2X as one would think.
The new Pocket 4K has a much higher 22watt average pier requirement, and it is the power load, along with the required voltage that drives an external power source. The internal battery is connected to the DC-DC board at s different tap, so it might have some if it’s voltage stepped up. So to answer your question as to which voltage is more efficient, the larger external 20-12 VDC input is only going to require down conversion, which is more more efficient, less loss, than up-conversion.
I use Dmitry’s Micro camera battery pack, which uses 4 18650 batteries and outputs around 14-16 VDC. It gives around a 2-3 hour run time, which works for me. For longer runs, I use a Anton Bauer 14.4 VDC Camera Battery on a Gold Mount plate, which runs for 6-10 hrs. I like the smaller form factor and reduced weight on Dmitry’s battery pack.
For Dmitry’s better pack, See
https://lavky.com/handmade/home-and-hob ... t=UW590888Cheers