I'd like to set the record straight on the issue of 'more power' when replacing a mechanical fan with an electric fan.
Generally speaking, with a mechanical fan the fan is spinning whenever the engine is running, and it takes power to run the fan. Let's throw around some numbers to illustrate what that means. Say that, at a given throttle opening and rpm, your engine is capable of delivering 150 HP at the crankshaft. If spinning the fan takes 1 HP, then there is only 149 HP left for other things, like accelerating the car. If you were running at a constant speed and load and you only need 149 HP, then eliminating the fan means that the motor's output can be dialed back to 148 HP by backing off a bit on the throttle, saving a little gas.
This is the basis of any power gain or economy gain. You are simply eliminating a parasitic loss, so there is more available to do something else - like accelerate faster - or less needed to keep something going - like cruising.
Now the above is changed slightly if you have a clutch fan as theoretically then can present less parasitic drag to the motor under certain conditions. The key, however, is that any mechanical fan presents a parasitic loss to the motor whenever it is spinning, EVEN IF THE AIR FLOW IS NOT REQUIRED AT THE MOMENT.
In cooler ambient conditions or at higher road speeds, enough air can move through the radiator core that you do not need the extra cooling afforded by the mechanical fan. So the fan provides 'extra' cooling and in return your thermostat just closes off some more coolant flow so the motor maintains the correct temperature. You have two systems fighting - one is trying to cool and the other is trying to heat. Clearly this is inefficient, so the industry moved to electric fans for these and all of the other reasons mentioned here.
An electric fan can provide high air flow at idle, when an idling motor with A/C on and so on needs extra help. Remember the old days whe you would pop into neutral and rev the motor at stoplights to provide extra cooling? That, too, was a waste. An electric fan solves this one, too.
Now here is the critical item that many lose sight of. An electric fan only 'saves' or 'gives more power' when it is off. Depending on your locale and driving environment, this can be a good chunk of the year. So you are running more efficiently during those periods.
Conversely, there are times the electric fan needs to run. When it does, it runs on electricity. The electricity comes from the battery, where it is replenished in the real-time by electricity generated by your alternator. The alternator requires power to generate electricity. The more electricity output, the more power required. This power comes from gasoline, which comes from your wallet.
An electric fan drawing, say, 30 amps at run is pulling over 360 amps (30 amps times 12 volts = 360 watts, and don't forget your motor is running at 14.4 volts, so the power is higher). Call it 400 watts. That's over 1/2 HP, and throwing in the inefficiencies of all the components (alternators are not 100% efficient) can get it up to 1 HP. Sound familiar? CFM is CFM and power is power, so when the fan is running you are dealing with a parasitic power loss just as you were with the original mechanical fan.
Averaged overall, which uses less power? It depends on many many variables. The design and pulley ratio of your mechanical fan, the rpm of the motor, the existence and efficiency of a viscous clutch, cfm, and on and on. With the electric fan, how much it draws at run, how much extra it draws at start-up (electric motors can draw twice as many amps to start up), how often the fan cycles on and off, the cfm, how often the fan runs at idle (putting out full cfm where a mechanical fan is putting out fewer cfm, therefore drawing less power), and on and on.
The only rule of thumb is that, in general, you are better off with an electric fan since most vehicles operate in scenarios where the constant draw of air by a mechanical fan is not needed OR the vehicle is operated under conditions where fan cooling is needed almost all the time regardless of engine rpm, providing better cooling since airflow is not tied to engine rpm. If the engineers know how much air flow there is all the time, independent of engine rpm, they can design tidier cooling systems, saving money. In this latter case there is no 'power' or 'efficiency' uplift, but there is improved cooling system behavior.
This was a long post and I introduced a lot of concepts. But that's how it works, and that's why electric fans are generally a good idea. Just don't expect miracles. They are not nitrous and they are not a Fish carburetor.