If we examine the power draw at the power inlet of the device (and thus rule out one advantage of 220Vac over 110Vac) then if an appliance draws 5mA when powered from 220Vac its power draw via P = I*V would equate to 220 * 0.005 = 1.1Watts. 
If we consider two types of loads.
- PASSIVE (resistive)
- ACTIVE (SMPS etc.)
A passive-type load would follow Ohm's law and thus a reduction in voltage would result in a reduction of current & equally a reduction in power. This is true for heaters, lightbulbs etc...
If you were to take a 5kW electric heater from the EU and plug it into a US 110Vac outlet you would find its output is 1.25kW (give or take) as the resistive load is drawing 11A instead of 22A.
Does this make 220V more or less efficient when viewing a passive load? neither because if you wanted a 5kW electric heater you would need to correctly acquire one for the operating voltage.
Active loads however are more constant power loads and thus a reduction in input voltage will be met with an increase in current draw as it attempts to maintain its operating point.
For you example of 220Vac @ 5mA == 1.1Watts. An active load would draw whatever current is required to satisfy its load's need. So if the voltage was reduced to 110Vac the current that would be drawn would be 10mA to meet the power needs of the active circuit (  is still applicable here)
Does this make 220Vac or 110Vac more efficient? Well this is where copper losses come into play & thus 110Vac would be less efficient than 220Vac systems.
 This is assuming that 5mA was drawn at unity displacement power factor & pure sinewave... it isn't in practice but for quick calculations to prove the concept.