How does the power setting on a microwave work? In general, how does the microwave power setting work? Is it a straight percentage of the maximum wattage or is it something less precise?

For example, would the time to cook something in a 700 watt microwave be the same as a 1000 watt at .7 power?

Is there any other major deciding factor in how one microwave cooks compared to another besides the power? (Assuming it is actually running at its listed power. Is it even possible for a microwave to drift off its posted power due to age or some other factor?)
The majority of microwaves cannot modulate their power output. The power setting in most microwaves simply turns the magnetron (microwave generator) off and in in cycles. So a power setting of .5 for 10 minutes would simply cycle the magnetron on and off every few seconds, with a total on time of 5 minutes. You can actually hear this occurring.

According to wikipedia, some newer microwaves can actually achieve a more or less constant level of reduced power using a technique called pulse-width modulation. I have never seen or used one of these though.

Microwave cooking is never very exact, so cooking something at 700 W vs 1000 W at .7 power would yield very different results. The only reliable way I've found in cooking things properly in different wattage microwave ovens is simple observation.