Yes, the efficiency levels for most classes of appliances vary greatly. Some factors that matter for a washing machine:
Did you know that some models/parts of the country, even on the cold water setting the washer will run a heater to get the water up above ground temperature? (Think about the alternative when doing laundry in Minnesota in the winter)
Is it using a shitty electric motor, or does it have a reasonable efficiency rating?
If a washing machine does not spin dry effectively, it increases the energy used to dry the clothes. Efficient water extraction is credited to the washer,
Dryers have CEf (combined energy factor) and most other appliances have plain EF (efficiency factor).