For a dryer, the energy consumption should be the same or less. The efficiency is a direct function of heat transfer between the source and the clothes. IME the US products work better because of their larger drum. At the end of the day, drying efficiency is not the total story, clothes which you do not have to iron are worth paying for(she tells me)!!
The new low temperature washing cycles are being used in the US as well as Europe and their spin cycle is IMO more effective at extracting water, so the efficiency is potentially more or less equal. Anyway, if you want clean bug free clothes, you need high temperatures and lots of clean water( or something toxic in it). If anybody tells you otherwise, they have never tried measuring the results of diluting acid with water, the more water, the weaker the acid concentration.
Regards Capitol