It's only really sensible to discuss fuel efficiencies in terms of the entire cooking system. Trying to talk about efficiency of a burner alone will get you nowhere.
So, we need to consider how well the burner is matched to the pan, and how much heat is wasted up the side of the pan. We also need to consider the windscreen, and the fuel wasted during any priming phases.
If you have a burner that runs hot (for example, the Rusty's burner getting through 2oz of fuel in 5 minutes), you need to have a system that can extract that high power output. Generally, this means a large area to the base of the pan, or a heat exchanger (that's the principle behind the JetBoil et al; pulling out heat from the flame that would otherwise be lost up the side of the pan). If the burner is too powerful for the pan to usefully take heat from the flame, then energy will be lost, and the efficiency will be low.
If you have a low power burner that burns fuel slowly, there's a chance that the losses from your cooking system to the environment are such that efficiency drops, but Tom Beasley did some useful experiments on boil time vs burn rate for gas stoves that seem to indicate that you have to go pretty slow for this effect to be noticed, but it depends on the operating environment (temperature, wind).
Without a windscreen, the lazy flame from an alcohol burner is likely to be blown about by breezes, thus losing more energy, reducing the efficiency. A windscreen also reflects heat back to the burner, causing it to evaporate fuel faster, thus making it burn hotter and faster (more powerfully). This can reduce boil time, but can also reduce efficiency if it makes the burner too powerful for the burner/pan/windscreen system.
If a burner requires a priming phase that prevents the pan being placed over the heat, then we're wasting fuel again. That's one reason why I don't like priming burners, not to mention the additional faff required; I like 'fire-and-forget' burners I can simply light and stick the pan over. Some priming burners are also fire-and-forget.
We also need to consider the 'flame gap'; how far we hold the pan above the burner. This depends on the type of burner. The pan can sometimes be too close, which 'quenches' or puts out the flame before all the fuel has burnt, or it can be too far away. Quenching is noticeable by a sweet, sickly smell of partial combustion products (you can find out what an alcohol burner 'exhaust' should smell like by running the burner with no windshield and no pan; it should smell simply warm and moist). The optimum (for fuel efficiency) flame gap can only be determined by experimentation with the entire stove system, in my experience.
Then, when doing fuel consumption comparisons, we need to make sure we're not comparing apples and oranges. Methanol has an energy content of 18.8kJ/ml, whereas ethanol has an energy content of 24.7kJ/ml, 31% more than methanol. So, when reading other people's fuel use reports, we need to make sure we understand what fuel they're using.
Oh, and we need to check water volumes, too; US stovies generally use 2 cups (473ml), whereas non-US stovies may use the near equivalent of 500ml. This issue of measures may also have an impact on the fuel volumes; most refer to 'ounces', which I've always taken as shorthand for 'US customary fluid ounce', 29.6ml, rather than the imperial fluid ounce, 28.4ml. The US fluid ounce is a somewhat strange measure, since one US fluid ounce of water doesn't weigh one ounce; no doubt the origin is lost in the mists of time, but must be based on a liquid with a density less than water (wine, possibly, but at what %age alcohol...?), or on a simple 3D volume. To confuse matters further, US food labelling regulations use a different definition of the fluid ounce (exactly 30ml). Wiki has a useful entry, as usual.
I've settled on a system based on a caldera clone and a trangia-style burner made from 250ml red bull cans, with a conic inner wall that allows the burner jets to be made on the rim of the pressed dimple, giving a conic flame ring that focuses on the centre of a small pan. It's made and operates in a similar way to the one Jim suggested earlier. BTW, here's my attempt at a set of instructions for building a burner of this type.
The clone provides an efficient windshield, holding hot gas close to the pan to encourage heat transfer, as well as a pan support. This system allows me to routinely boil 500ml water with 15ml UK-spec 95/5 ethanol/methanol 'methylated spirits' (i.e. mostly ethanol). If I'm boiling more or less water, I can scale the amount of fuel I use and get a boil as expected.
Having spent a lot of time and effort playing with many stove designs, it's disheartening to find that one of the simplest is also just about as efficient; take a 250ml red bull can, and make a simple, open-cup burner by cutting a suitable height cup off the bottom; an inch, say. No priming, no vapour chamber, no fancy jets; just a simple puddle of burning alcohol. Obviously, it needs something to hold the pan above the burner to allow the fuel to burn.
It's interesting that both Rusty and Dan are using the same Cat Stove design, and yet one uses twice the fuel of the other (bear in mind my comments about comparing fuels). It would thus be very instructive to see the exact setups that both use, so we may be able to figure out just how this discrepancy arises, and where the energy is lost/is saved.