Old recessed radiators with reflector foil

I think you are saying that you have two zones on one boiler, each fed by its own pump and thermostat (i.e. the radiators have been converted to hot water). My answer is based on this assumption.

Since they're both on the same boiler, the water is heated with equal fuel efficiency.

The two loops probably are different in how efficiently they transfer that heat to the room. Low efficiency in transferring heat to the room will decrease the heating capacity of your boiler, which is a problem if you can't get the house warm enough on a cold night. But as long as you're keeping up with heat demand, efficiency in transferring heat doesn't make a difference with fuel usage. (You can tell how efficient they are in transferring heat to the room by feeling the temperature at the end of the loop -- if it's pretty cold, the heat was transferred to the room very well)

So, the answer is that you should set the thermostats to the lowest temperature where you're comfortable. Your addition from 2000 likely has a lot more insulation than the original 1939 house (in 2000 the building code required a lot of insulation, 1939 not so much), so if you want to pick the more efficient one to heat, heat the addition not the main house. It will be more efficient because you'll lose less heat because of the greater insulation.

Statistics? I'd argue this is a misuse of the word, unless you are asking what is the fraction of photons reflected by the reflective surface. Since that truly is a probabilistic question, we could indeed compute statistics on the distribution of such reflections.

Yes, this is not just a theory. Heat is transmitted in several ways. One such way is convection. So the radiator heats the air around it, which will rise, displaced by heavier cool air from the rest of the room. These convective air currents cause a transmission of heat from the radiator into the room.

A second way that heat is transmitted is by radiation. Infrared photons will carry off energy (heat) from the radiator. Some of these photons land on the wall behind the radiator. If the wall absorbs them, then it will get warmer. So the trick is to put a reflecting surface in the way. A SHINY metallic surface is such a solution, a heat mirror. Thus a shiny metal foil will suffice. Even a regular mirror, which is simply a piece of glass with a metallized reflective back surface that reflects light, will suffice.