A diode string dropping voltage from 16 to 12 will use the same wattage as a resistors,however it will always maintain about 12 volts regardless of load so it acts in effect like a variable resistor. For a DC single string dropper the the wattage used would be the number of diodes times .6 times the amperage drawn.
A single diode dropping the voltage in effect by half (a little less due to the forward drop of the diode) will use much less wattage than the resistor. The wattage used would be only the forward drop of the diode,about .6 times the amperage drawn. The reverse current is completely blocked with no current flow in the opposite direction. A small insignificant amount of heat might be generated blocking it in reverse. A resistor of half the load value would use as much amperage as the load itself. So with this half wave dimming method we kind of get a free lunch.
Dale H