A PWM circuit will use less power at lower speeds.
The original resistor will, as well, but is not as efficient as the PWM units. (Adding the resistance into the circuit decreases the current, per Ohm's law, which means less power consumed.) Ideally the switching devices in a PWM circuit will dissipate no power, since they are either fully on or fully off with no time spent in between where they act as a resistive divider with the load. For practical circuits, that's not quite achievable since semiconductor switching times are not truly instantaneous and since the on state has a bit of impedance, but it gets quite close.
The unit you had that failed was most likely some sort of a PWM controller. It may well have failed due to the lack of a big enough heat sink, allowing the switching transistor to overheat.