Which one is correct for this power consumption estimation?
The correct way to measure power consumption when the supply voltage is DC (and constant) is to multiply the voltage by the average current and forget about trying to use RMS current because that would give an incorrect answer.

If you consider that the current might be a sine wave superimposed on a DC current (just as an example) and you multiplied each individually by the DC voltage, you would get two numbers where one was the average power (the right answer) and the other is another sinewave (Vcc times higher in amplitude) whose average power value was zero hence, that second number does not contribute to average power.