How can 12 V halogen downlights be much more efficient than 220 V ones?
This gets into efficacy/usefulness verses efficiency and the important fact that less voltage is far more stabler.

If you look closely:


12V 50W energy consumption = 53 kWh/1000h
240V 50W energy consumption = 50 kWh/1000h


Thus the 240V 50W is 3kWh/1000h more efficient in energy consumption.

However the 240V 50W has half the life span of the 12V


12V 50W number of switching cycles= 50000
240V 50W number of switching cycles  = 25000


Thus the efficiency you would gain is nullified due to the decreased lifespan.

Next compare the luminous intensity


12V 50W luminous intensity = 1450
240V 50W luminous intensity  = 900


By far the 12V has a much greater efficacy to efficiency ratio.

Now to explain why

Voltage is the rate/speed/pressure of electrical phenomenon.  

On average 12 volts is plenty fast to illuminate a 50 Watt incandescent or halogen. 

Increasing the voltage beyond this point as you can see does little help as the efficacy "usefulness" of the bulb to achieve desired illumination in relation to the efficient use of energy it requires is most satisfactory at 12 Volts.

As an experiment, take a 9 volt battery and touch the two prongs to a 20 watt halogen MR16 or MR11.  The voltage required to reach the desired efficacy is very little, and less voltage/pressure is a good thing.