I always time my stoves from the moment the match hits the fuel until I reach a boil.
I'm not sure what the original question was really asking. If the question is "what's the lightest stove set-up that will boil X-cups of water for a three day trip", that is quite a different question to "which is the most fuel efficient stove"?.
Temperature and wind conditions aside (these are big factors affecting the answer), it is hard to imagine how something like the Reactor could be the lightest option, even though 'fuel efficient'. The base weight of the stove drags it's weight efficiency down to the bottom of the list for a short trip, unless you encounter horrific winds without any shelter. Same for butane. You would really have to save a lot of fuel for the weight of the stove and empty canister to be competitive with a basic alcohol set-up over three days (again depending on how much boiled, what the weather is doing, etc…).
I have been getting almost complete fuel recovery (minus 1 gram) using either the featherfire or the trail designs 12-10 with snuffer cap and 'suck-back' nozzle. This makes the 12-10 plus caldera very weight efficient for sorter trips. For longer trips I would be tempted to go with a BushBuddy and back-up Esbits for maximum weight plus fuel economy.
If you're are merely worried about reducing carbon emmissions, then the Reactor or Jetboil are a better bet for any length trip (though the carbon cost of making those disposable canisters is unclear…).
Then there is the question of convenience and speed. A basic butane stove is extremely convenient to setup and boil water quickly in a range of conditions. The heat exchanger of the Reactor or Jetboil increases the speed, not sure about the convenience. Also along the lines of 'convenience' is how to pack a Caldera Cone to keep it safe between uses.
There's a lot that can go into deciding on a cook system. The best bet is to see if you can borrow some different setups and test them for yourself, in real situations cooking the volumes you want to cook.