They use (in our case) less water than hand washing (some are remarkably efficient) and the energy use depends on whether they are hot or cold fill and how your domestic water is heated. However, the convenience is immense.
We only got one 4 years ago when Mrs Norm's hand was broken in a car accident, we wouldn't think of going back now, though.
Oh, and the energy use is, IMO, one of those things that everyone talks about but is pretty small in the big picture of household expenses - the difference between a good one and a great one likely comes down to under 20p a week.