In reply to dunc56:
All other things being equal, a cordless device would use more energy due to inefficiencies in the battery charging process.
My limited experience of cordless cleaners however is that:
1) They're lower power than corded. I do not know enough to predict if a lower power cleaner uses more or less energy overall, and suspect this depends on myriad factors.
2) They tend to have a hand activated power switch in the grip, encouraging the user to turn them off when moving from place to place compared to a cabled cleaner. This alteration of user behaviour could potentially save a lot of energy.