I would agree with food that the windscreen is the most important point, however the area of the bottom of the pan does make a big difference, the bigger the better because you get more square inches to transfer heat in, AND the surface to volume ratio of the larger vessel/windscreen system is smaller so there is less area (per volume of water) to radiate heat out or to lose heat through conduction to cold wind, so of course there are many curves of this complex function that intersect someplace at an optimal configuration.

I would argue that two 12 ounce boils takes less energy than one 24 ounce based on two things, according to the laws of thermodynamics the most heat will transfer when the temperature difference is maximum, however the difference in the flame temperature and the temperature of a pot is not that great between a cold pot and a hot pot, however if there is condensation on a cold pot and it drips into or interferes with the heat source it may lessen the heat output (thus perhaps this is where foods idea comes from) of the stove/fire. Also a flame which does not get to burn fully before being cooled (by the pan) will generate more carbon monoxide and I've read that most stoves have too low of pot supports and raising the pot up an inch higher will let the flame burn more completely before its cooled, since its the colimn of rising hot air that actually carries the heat.

All of this suggests that starting with a smaller amount of water and then adding more after the original amount is warm might be the most efficient as the pan could be warmed enough at first to prevent condensation on the bottom of it.

Small pots are not efficient and the very worst pot I ever measured was the MSR kettle. I would assume that the factors making it inefficient would also apply to all small bottom pots.

Also the difference between laboratory testing and real world usage is great. It can take up to 45 minutes in a wind without a windscreen to accomplish what can be done in 3 minutes inside without a windscreen. You have to assume that in cold weather it will take more energy. The more heat your stove puts out and the quicker you can heat your water the less heat will be lost to the air, however a stove may become less efficient if it puts out too much.

It is my own belief based on controlled experiments inside and outside in various conditions (and lots of experience cooking in the cold without taking data) that a covered pan with a heat exchanger with a good windscreen coming all of the way to the top of the pan, but with good air supply to the burner, will be most efficient at between 10,000 and 15,000 Btu, and that insulating the lids makes no measureable difference. There may simply be too big of flames extending above the top of the pan at 15,000 Btu and that energy is of course lost, but if the water in the pan is deep enough to pick up energy from the sides as well as the bottom it increases the heat transfer area. I think a 2 liter pan has about the optimal area and I always use a 2 liter pan for snow melting unless I am alone and don't really care.
Jim YMMV