A. Fortunately guys it is not as tricky as it first appears. I knew that we have just the service down here in Australia (and New Zealand) that you seem to be seeking. It's been going for about 20 years as the Energy Rating Label. (Look here to see how they rate dryers, for example.)
The government requires all suppliers of whitegoods (washing machines, dryers, fridges, freezers and so on) to have their appliances energy rated and a sticker applied to the goods in the store. Back in "the good old days" you could also pick up a free printed brochure comparing all similar products together. This chart is now available online. In more recent years they have also added beige goods (computers, printers and photocopiers, etc) and brown goods (home electronics such as TVs, audio products, and DVD players), so called because once upon a time all such things came in fake timber cabinets. These latter two have their own site under the Energy Star program. This is an international program, so I was pretty confident there was a similar deal in the US.
And there is. Also under the Energy Star banner. Here they rank many products, including washing machines. They suggest that "compared to a model manufactured before 1994, an Energy Star qualified clothes washer can save up to $110 [USD] per year on your utility bills."
But unlike Australasian one there is no such comparison for dyers. Damn. The US EPA, who run that site, believe "most dryers use similar amounts of energy." so don't label them (see next para). But do offer some tips on how to limit their demand on the grid. These include air dying clothes, selecting a dryer with a moisture selector so it automatically turns off when contents are dry and choosing high spin cycle on your washer so clothes as close to dry as possible when they go in the thing.
The Australasian chart shows a spread of dryers using energy in the realm of 82 to 480 kWh per 52 uses. Admittedly this is for capacity variances of 2 litres to 9 litres of soggy laundry, but does indicate that not all dryers are created equal.
With your washing machine selection, a front loader is likely to use bucketloads less water and energy. And spin your clothes drier, so they spend less time in the dryer, with a resultant decrease in energy load. Also with a front loader you can mount the dryer directly above, saving space. The down side is generally a longer time for wash cycles. Some clever front loaders can do double service as dryers. If you can afford a European branded front loader, you may find they are more effective. The often smaller size of European dwellings has meant washers are commonly located in the kitchen and issues like noise, stability and durability become more obvious in a product under ones nose.
The Energy Star site in the US has downloadable charts which even show you the water usage for each machine - something we wish the Aussie one also covered, even if they do show the difference between a hot and cold water wash. Obviously cold washing uses heaps less energy, whether heated by your water system, or the washing machine itself.
(In Australia we have separate water usage classification for washing machines, which is alas only a voluntary program. It's known as the National Water Conservation Rating and Labelling Scheme. In one of their brochures they suggest a front loader can save 135 litres (36 gallons) of water compared to an old top loader machine. That's per wash, not per year!)
Well, Rob and Cat, trust we have contributed something useful to your search for greener laundry. No doubt TH readers also have thoughts on what specific machines have worked best (or not so) for them.