6 of 6 Clarification

I think the primary considerations are convenience (how much effort is it to set up and use the system?) and time spent (how long does the system take to heat the water?).

A standard electric stove can have 2500W elements, and most of this energy will go into a kettle sitting on the element and thus heat the water. Even a big built-in microwave won't be rated at much more than 1000W, and a fair percentage of that is wasted in heating the magnetron (I've found citations of 30% to 50% wasted power). So, all else being equal, a kettle on a stove will heat a body of water 2-4 times as fast as a microwave oven.

If you're instead talking about electric kettles, then in the US (120VAC) they're 1000W to 1750W with very high efficiency, so they'll still be faster than anything but a stove or a commercial microwave. In the lands with 220VAC power, electric kettles can be up to 3000W, which would be even faster than a stove-top kettle.

With a mug of water the convenience of a microwave may outweigh the lost time, but if you're heating a liter or more of water then you probably want to pull out that kettle.