For fan clutches, we generally assume that unlocked is usually in the range of 10-20% RPM and locked is in the range of 70-80% (sometimes 90% for HD clutches) of water pump shaft speed. In reality, the percentage probably actually varies with the engine speed in a non-linear fashion due to the non-linear torque relationship of fan speed versus RPM. But even using these basic assumptions, it's pretty easy to demonstrate the difference between them.
A fun fact is that the fan clutch is actually less mechanically efficient unlocked than locked. The torque across the fan clutch is conserved (in steady-state), but since RPM in does not equal RPM out, a significant portion of shaft power is simply converted to heat. (Hence why fan clutches have cooling fins.)
If we're assuming 20% for an unlocked clutch, it it takes say 0.02 horsepower to spin the fan at that speed, we're also burning up 0.08 horsepower as heat in the clutch, for a total of 0.10 horsepower. Meanwhile, if we lock it at that same speed (assuming 80% for locked), the fan affinity laws will tell us that the 4x in shaft speed will result in 64x the power consumption and 16x the torque for the fan itself. Meanwhile for the clutch, since it only slips at a quarter of the RPM, the 16x torque only means a 4x increase in power loss in the clutch. So in this case, the fan now takes 1.28 horsepower, and the clutch now burns up 0.32 horsepower, for a total of 1.60 horsepower. So in terms of mechanical efficiency, the clutch fan is only 20% efficient unlocked, but is 80% efficient locked. However, power consumption is still far higher with the locked clutch.
(The horsepower units here are of arbitrary magnitude.)
Meanwhile, the electric fan has a relatively fixed energy loss ratio largely driven by the alternator and the motor itself. Using the marginal efficiency for the alternator (not overall efficiency, because it already exists), multiplied by the overall efficiency of the fan motor, you usually end up with about 50-60% overall efficiency ratio in converting rotational energy at the engine to rotational energy at the fan.
Interestingly, because alternators will react to maintain constant power output, shaft torque actually drops inversely with engine RPM, unlike a mechanical fan, in which it increases with the square of engine RPM.
The final distinct advantage of an electric fan is that the control scheme can be way more complex than for a clutch fan. This is the biggest driver of efficiency in OEM applications. Since the control scheme can be more complex, you can make the fan run only when needed, and only as much as needed. So there is significantly less energy wasted creating excess airflow.