(From this Reddit thread)
Heating 2 liters of water from 20 C to 100 C takes 669 kJ of energy. Note that this is just the heating, getting the water to boil takes a bit more. Kettles are typically very efficient, almost all electrical energy is converted to heat by the heating element (losses elsewhere are quite small) and the process is fast enough that there isn’t much time for the heated water to lose heat to the environment.
If you use a 1 kW microwave for 1 minute, then that’s 60 kJ of energy. However, microwave ovens are not 100% efficient, so to deliver 1 kW of heating power, they draw more than that from the wall socket. The excess is lost through heating of the transformers and internal circuitry. I couldn’t quickly find detailed lists of microwave oven efficiency ratings, but I found a blog post (http://www.triplepundit.com/2007/01/askpablo-microwave-efficiency/) where someone measured the power draw at the wall of this 900 W microwave oven and found it to draw 43% more than it’s rating. Applying this to the previously found 60 kJ, we can expect a power consumption of around 86 kJ.
So the microwave approach is considerably more efficient than the kettle approach. Which is hardly surprising, since you only heat one eigth of the amount of water. Note also that with 1 kW for 1 minute, you’re only heating your water by at most 57 degrees Celsius. And that’s assuming the energy is only absorbed by the water and that there are no losses during the process.
If you were to do a more fair comparison, the same amount of water being heated by the same amount (as measured in temperature difference between start and end), the kettle should win out since it’s very hard to beat the efficiency of a decent kettle.
Result: Win for kettles!