I think there many be a little difference in our definitions. Input power is from the battery to the voltage converter. Output power is from the converter to the coil. Thermal efficiency of the coil is a completely different conversation, but the efficiency of the converter is very pertinent to this conversation.
A battery does not provide power, only voltage, and the output from the converter is voltage, not power. Power doesn't enter into the equation until the current passes through the resistor(coil)
Sorry, this isn't thoery. These are the laws of physics. I don't expect anyone to take my word for it. Please, research it yourself if you feel inclined. Just remember that the only way to truely learn is to accept that what you think you know could possibly be wrong. I once thought along the same lines as you, and SoberSnyper, and frankly the majority of this forum. Then I researched, I learned, I tested, and I proved it to myself. The earth was once thought to be flat and the center of the universe.
The only thing that has been demonstrated is that people claim to get better battery life with a certain configuration, and I acknowledge that by saying they are using thier PV in a configuration that runs more efficient. No one has posted any tested, measured, and qualified proof that I have seen. It's all been conjecture. I have proven this to myself by measuring both input and output voltage and current and calculating efficiency loss in certain configurations.
If I am using a Vamo, set to 10 watts, will I get more vaping time with a 1.5 ohm coil or with a 3 ohm coil? It is a simple question, the answer should be easy to conclude.
Also, using a mechanical mod with a low res atty to compare to a VV/VW device with a standard or high res atty is an invalid comparison as the VV/VW device is providing a constant supply of voltage and the mechanical mod starts with 4.2 volts of a freshly charged battery and is being continually drained while vaping. As the voltage of the battery decreases, so does the current, as a result, the power of the circuit is continually decreasing as you are vaping.