I would imagine that it would be slightly less efficient to keep some of your water hot while waiting to use it than to heat it to temp as needed. For example, heating all 11 gallons to mash temp, then keeping the unused portion at sparge temp during the mash would cost some energy over heating the sparge water "just in time". And I don't think that heating larger volumes of water is inherently any more efficient (energy required per gallon per degree of temp) that heating smaller volumes. Also, one particular individual burner/pot (volume and geometry) set-up might have greater efficiency than another. But, at least for me, the convenience of having the water at the proper temp when I need it outweighs the slight (I imagine) efficiency costs.
I should note that I brew in my kitchen, using a gas stove. Once I get to the temp I want, I can turn the gas flame down to a "maintenance" level for as long as I need to hold that temp. I'm not sure how easy it would be to do that outside on a propane burner, or with an electric heater setup for that matter.