The contestants:

A Homigrand electric kettle, rated as drawing 1000W.

A Faberware stainless steel pot on a GE Spectra glass-top resistive electric stove (JBP66BBWH). The 6" burner I used is rated as drawing 1500W.

I filled them both with a quart (about a liter) of water, which was near the capacity of the kettle, and verified that both were starting at the same temperature (62F):

The thermometer is wet in the second picture because I accidentally dropped it into the pot, but it's rated IP66 and didn't mind.

I started them simultaneously, and waited. The kettle took 6:32 to reach its automatic shutoff, and I measured at at 212F. The pot took 7:20 until I guessed it was boiling from the sound, and it also measured 212F. So the pot is about 12% slower despite using 50% more power, so 68% more energy. Still, it's only 0.18kWh vs 0.11kWh which at $0.21/kWh is $0.04 vs $0.02 so I'm more interested in the time difference. Even that is small enough, however, that if what I want is boiling water in a pot to cook something I think I'll still use the pot.

One exception, which I was already doing, is that when I'm making pasta in a hurry, typically for the kids, I'll put half the water in each and then pour the kettle into the pot when it boils. (If I had been dividing the water exactly I'd have already known the answer to this question!) The main gains here are from parallelism, however, not efficiency.

This does make me wonder whether Americans (or British expats) ever put dedicated 240V outlets in their kitchens so they can use ~2-3x more powerful European kettles?