My apologies for using the old 'water pipe' analogy as it's not 100% accurate, but it sure makes a good mental image...
(we'll be talking 'DC' for now)
Voltage is the difference in electrical potential between two points and the strength of the electrical charge on the electrons flowing in a circuit. Amperage is the volume of electrons flowing in a circuit. Electrical power, the measure of useful 'work', is measured in Watts and calculated by multiplying voltage times current.
This much you know.
So, a circuit drawing 100 volts at 1 amp consumes 100 watts of power, as does a circuit drawing 1 volt at 100 amps, or another circuit drawing 10 volts at 10 amps, or 20 volts at 5 amps. It's all the same number of watts. How much of this power is actually converted into doing something useful is determined by the overall efficiency of a circuit and the usual design compromises. We'll touch on that later.
Let's imagine a thin pipe that has 1 square inch of inside area that we'll put 100 pounds of water pressure behind. We'd see a thin stream of water that squirts waaay out there, and this is analagous to 100 volts at 1 amp. If we put a turbine or paddle wheel in the stream of water exiting the pipe, it would develop a modest amount of torque at a high RPM that could be used to power something.
That's our wattage. As for the differential between two points, we'd measure 100 PSI at the tip of the pipe, but near-zero once the water hits the ground. A 100 pound differential at each end of the stream.
Then, let's take a pipe with 100 square inches of internal area and put one pound of pressure behind it. Not much squirt, but it's a real soaker, and we have a one pound differential in pressure. If the analogy is perfect, we'd have the same amount of power available from either arrangement at our turbine or paddle wheel device, but the second example would yield higher torque at a lower RPM.
The thin pipe squirts 'harder' with not much water (high voltage, low current) while the thick pipe has much less squirt but delivers a much higher volume of water to our device or 'load' (low voltage, high current).
Which is better? A relatively few highly motivated electrons, or a large volume of under-achieving electrons?
Neither. It depends on the situation. Different techniques make more sense in different applications.
F'rinstance: Why not design cars with 120 volt AC electrical systems? Great idea, you could load up your old Magnavox color TV in the back seat to keep the kids amused while using cheap household bulbs for the lighting. Heck of an idea. But, how large and heavy would the 120 volt AC battery need to be for the starter? And where do I buy an AC battery? Could this be dangerous on rainy days? You betcha'! Better to go low voltage / high current in a car.
As for efficiency, why does your local power company run 38,000 volts or better on their high-tension lines when you need only 120 volts? And why do PA systems prefer to run '70 Volt' (600 ohm) outputs instead of the 8 ohms or less commonly found in loud speakers?
If there's a 50 volt drop in the wiring between you and the power plant 25 miles away, would you rather lose 50 volts out of 120, or out of 38,000? Yup. Figure the percentages, and the higher voltage distribution is far more efficient. As for the PA system, if we have 16 ohms of resistance in the long wire we ran to the back of the hall, and we're using 8 ohm speakers, that's 24 ohms total resistance in the circuit with only 1/3 of the power dissipated in the speaker. (16 ohms in the wire, 8 in the speaker, and I'm ignoring the impedance match for the sake of simplicity) This means a 100 watt amplifier could deliver only 33.3 watts to the speaker and waste the rest heating the wire.
What happens if we run 600 ohms in the system with the same 16 ohms in the wiring? The percentage of loss becomes trivial, and the cost of the matching transformer at the speaker is far less than the 300 watt amplifier needed to compensate for the wiring losses.
You know an electron is an electron is an electron. But, depending on the circuit, electrons can carry a high differential of charge that gets a lot of work done with a relatively small number. Or, you can design for a larger number of less-energetic electrons.
Either way, you get the same amount of work done.
Hope this helps.
And, don't forget: The mightiest living things in the jungle are the largest of trees that can lift water hundreds of feet in the air. And the only living thing a tree fears is one of the very smallest that can lift almost nothing...
So, which is more powerful?