Some factors to consider are speed, power consumption and the hotest heat
Speed => edge goes to microwave, hands down. 90 seconds for a glass of water compared to 5 minutes or more on a stove.
power consumption => depends on what type of stove you're using. A gas stove would certainly use less energy, but an electric stove would probably not. I will go with kettle on this one.
hottest => kettle, a stove can get food much hotter than any microwave can.
Hmm, any other factors?
Safest => microwave, but don't put your head in there.
Easiest => kettle is easier because it makes a sound when the water is boiling. Kettle.
Cost => usually the microwave and stove come as a package, but when separate the stove costs more. I think the stove has a higher average cost per month. Microwave.
I would say that using a kettle to boil water is better than using a microwave. better quality overall, but if you want speed, go with the microwave.