Again, it's the automatic defrost feature on modern fridges that can be the big energy guzzler.
Example: when I bought this house in 1997, it came with a GE SXS fridge, circa 1978. I checked with GE and it was rated to consume over 1700 KWh/yr. I liked its ice maker (nice cubes) but replaced it with a KA SXS that uses about 640 KWh/yr. At the time, KA and Whirlpool were at the forefront of energy efficient fridges for the consumer market. Better insulation, more efficient lower power compressors, and better implementation of auto defrost. So for the same capacity, my new (in 2000) fridge used about 1/3 the energy of the older one.
Now in the garage I have an even older GE, circa 1948. It's probably about 16 cu ft with one of those tiny freezers that might fit a half gallon of ice cream and an ice cube tray. But as I recall when I checked, it uses about 400 KWh/yr. Again, very thick insulation, and no automatic defrost whatsoever.
Newer fridges appear to be even more energy efficient. One drawback is that they all now use non CFC refrigerants, using flammable hydrocarbons instead. This may be better for the environment but it's also more of a safety hazard for consumers.
My 15 cu ft Kenmore chest freezer uses about 350 KWh/yr. It's manual defrost, but is one of the few that has a flash defrost feature, which is great. You still have to empty it out, but when you pull a little knob in the lid, it reverses the refrigerant flow and sends hot refrigerant through the coils, which melt the accumulated ice relatively quickly. It's a great feature but kind of rare. Alternatively one could use a hair dryer or (carefully) a heat gun to get rid of the ice buildup. I find I only need to do a defrost about once a year. Usually I wait for fall when the temps in the enclosed patio where it resides are lower so that the relocated items don't thaw so quickly.