The most important feature for sound reduction is the amount of insulation around the washing tub. Other features which reduce sound include insulation in the door, toe panel and access panels. Some models even have very quiet motors and vibration-absorbing material linked to the motor. The amount of energy you save is basically up to you. Just buying a dishwasher will probably reduce your energy costs.
Many studies show that new dishwashers use less hot water and energy than washing by hand.
And, if you don't prewash, you'll save even more. Another big factor in saving energy is your choice of wash cycle. If you choose the highest wash setting, you're going to use more hot water and energy, so you'll want enough washing cycle options to fit different loads. The number of cycle options varies among models and manufacturers, from two cycles to seven. One feature that can help save energy is a delay start control.