I steam vegetables in large batches (up to 3 lbs) in covered Pyrex bowls in our large microwave. The microwave is 1800W, and steams the vegetables well in 4-6 minutes (depending on the vegetable...about 5 minutes for broccoli, which is fibrous). Bringing approximately 2" of water in an 8qt stockpot (the amount you'll likely need to heat in order to have the entire batch remain over steam before evaporating all the water)to a boil, plus steaming 3 lbs of broccoli in a steamer insert will take about 6 minutes on my stove on the 12,000BTU/hr gas burner.
So, that's 1800W x 5 min vs 12,000BTU/hr x 6 min
1W = 3.41BTU/hr
Converting the BTU/hr to watts that becomes
1800W x 5 min vs 3517W x 6 min
Since 1 W = 1Joule/second, the two energy expenditures are:
-Microwave: 1800J/s x 300s = 540,000 joules
-Stove: 3517 x 1,266,120 joules, more than twice the cost.
Stoves send a great deal of energy up the sides of the pans and into the air, where it is lost. Microwaves send nearly all their energy into the food. This means that in nearly every case, steaming in the microwave is more energy efficient.