Wait a minute. Power is 'watts' or 'joules/second'. Energy is 'watt seconds or hours'. That's power x time. The unit mw/hr would read 'milliwatts per hour', which is not correct at all. The joule is the unit for energy. A joule/s is a watt.
Electrical generating plants are usually rated in 'megawatts' or 'MW' with a capital M. This is power. Power is only the time RATE at which electical energy is produced/used. You don't buy 'power', you buy 'energy'. Energy is measured in watts times time, or 'watt hours'. This is sometimes written as 'watt-hours' but then some folks think the dash is a minus sign, which it isn't.
A 100 Watt light bulb isn't more 'powerful' than a 60 watt bulb. Things can't 'have' power. They can only 'use' energy at higher or lower rates. 100 Watts means the bulb uses energy at the rate of 100 joules per second. Every second it is on, it uses 100 joules. In one hour, it uses 360 000 joules of energy.
This is an excellent post. It shows knowledge of physics and explains things clearly and concisely. You have brought the discussion of a technical subject to the right level of detail without being pedantic.
Most people have no understanding of physics and everyday conversation doesn't have the same precise definitions for ideas like power and energy and motion. For example try to tell someone that the brake pedal in their car is an accelerator. In physics it is an accelerator as is the steering wheel when going around a corner, but neither of these devices will ever be an accelerator in common conversation.
In the imagination of popular culture, a 100 Watt bulb will always be more powerful than a 60 Watt one. This is often a source of confusion when moving to scientific subjects.