When we decrease the speed of a fan, the power consumption by it also decrease.
In regulator with resistance, the power saved is less than compared to the regulator with a triac. This is because in resistive regulators, a resistance is added in 'series' with the fan, thus keeping the voltage fixed. It reduces the current flow to the load. But it itself dissipates much heat, thus wasting some energy.
In regulator with triac, there is a break in voltage supply by triac firing, thus causing less energy supply to the fan. The triac doesn't hampers the supply by means of resistance, but by switching off the triac gate after a 'certain time', when the AC wave rises or falls from 0V. It itself doesn't wastes much energy and is the most efficient way of regulating a fan.
Thus, a regulator really saves electricity bill. As slow you run the fan, as low it consumes power...