On this side of the pond
We have a Liebherr chest freezer from some time in the early 2000s and a small build in upright IKEA from 2012 I think.
When the build in AEG that came with the kitchen in 1987 broke, I emailed them about the consumption, and the reply stated it uses about 1kWh per day. The new replacement, while being in the lower end of todays efficency ratings (A+ on a scale from A to A+++), uses half that, saveing us about 5€ a month.
And that is on a really small model with only about 3.6ft³.
However, when we were deciding if we should replace our ~10 year old build in fridge after one of the hinges broke, it turns out that we would only save like 1-2€ a month with a A+++ rated fridge.
So, I think with really old cooling appliances, savings can be really big.
On the topic of NoFrost freezers (that's what hey are called here), a sales person here once made a really good point:
For a freezer that is used as a long term storage and thus isn't opend that often, there is verry little air exchange happening that could cause ice buildup. There, automatic defrosting can have negative effects due to temperature fluctuations and the higher energy usage of the defrost cycles.
For freezers opend more frequenly, the slightly reduced holding time of food dosen't matter as much and due to the faster ice buildup from more frequent opening, a NoFrost system has less of an impact on the efficency due to the better efficency of heat exchange without ice buildup.
On inverters: I know that a lot of really high efficency fridges and freezers over here do use inverter controlled compressors. Most give a 10 year warranty on compressor and inverter.
In theory, a well controlled inverter cooling system can keep food fresher for longer with less energy usage.
Instead of cycleing on and off, an inverter system is usually designed to run non-stop, with the lowest power setting being just enough to compensate for heat loss via insulation. That keps the temperature really consistent in theory and saves energy and wear as normal compressors have high start-up currents.
If the door is opend and\or fresh food is added, power is ramped up immediatley and temperature loss is compensated rapidly.
Some systems go as far as to learn the day\night cycle: The first few days after turning on, they run with a slightly higher temperature reserve and check when the doors are opend and when not. Then, they adapt and allow for bigger temperature tollerances during phases of the day when doors are less likely to be opend and thus need lower compressor power during that time.
