Series Regulation

[kchriste]

With 12V also the average current was 20mA only. But it was continuous. Here it is 40mA with 50% duty cycle keeping the average as 20mA. So brightness should be same if the light O/P of LED varies proportionately with current (which may not be true in this case as audioguru pointed out).
Right?

That is correct except that the LED's average brightness, at the higher peak currents caused by PWM, is not as bright as the equivalent DC current. My point is that you won't save any power this way either. Go with the buck boost regulator as mentioned by others here if you want to save power.