Avoid thermoelectric units if you are interested in electrical efficiency. These work on the same principles as thermoelectric coolers for use in cars, and are a lot less energy efficient than the compressor-based units. (They are quieter.)
A standard dehumidifier is basically just an air conditioner or a refrigerator where the air moves over the evaporator (which cools it, condensing the moisture) and then over the condenser (which warms it back up); or, int he case of a thermoelectric unit, over the opposite sides of a peltier junction heat pump. If the ambient temperature is low enough, there's not much dehumidification that can possibly be done because the cooling results in frost buildup. Ambient temperatures in the 50's or 60's are fine (though efficiency goes up with warmer temperatures) and typical of basements; temperatures in the 30's are more of a lost cause, and obviously in subfreezing temperatures the system can't work at all.