Now...I understand how if, instead of wiring the 8 in series, I were to wire them in 2 parallel circuits each with 4 LEDS off the SAME power supply, then efficiency would drop, since I'd have to drop far more voltage in the resistors.

BUT, suppose I were to replace the original battery with one of exactly half the voltage and re-calculate the resistors. now each should drop the same 25% as in the original series example. Now I have two circuits consuming the same amount of power and with the same efficiency, (I THINK) Except one is half the current at double the volts, and one is double the current at half the voltage. I guess with an ideal power supply, it doesn't matter, but with batteries, would one be preferred over the other? When power consumption is the same, is it better to use a battery with double the voltage, to get half the current draw by wiring all LEDs in series, is the reverse true, or does it not matter either way?