Edwin Pawlowski writes:

I agree that a frost free may use a bit more, but I'm betting it is
the tiniest bit more.

It's not tiny.

Consider just the ice making process in a frost-free refrigerator.

First, you pay to pump the heat of fusion to make the ice to start with,
with some heat of vaporization from the liquid.

Second, you pay for a fan motor to circulate air in the frost-free
design, rather than using convection as in the old way.

Third, you pump the heat of fusion *and* vaporization, as a substantial
amount of the made ice is sublimated by the circulating air, ice turning
into vapor, as your ice cubes shrink.

Fourth, you pay for the heat of fusion and vaporization, to condense the
sublimated water vapor onto the evaporator coils.

Fifth, you pay the heat of fusion to melt the frost off the evaporator,
the liquid frost water going into a pan at the bottom of the unit.

Sixth, you pay to evaporate this frost water out of the pan into the
house air.

Seventh, you pay yet again to condense this vapor out of the house air
via your air conditioner, and finally get this waste out of the house.

So in making ice in your frost-free, quite a lot goes into wasted ice
making several energy-hogging thermodynamic round trips from liquid
and/or solid to vapor.

Try turning off your frost-free ice maker, and removing all exposed ice
from the freezer. You'll be amazed how much lower your duty cycle is.
Ice making and ice waste makes up a large percentage of frost-free
energy costs, and doesn't quite make it into the federal formulas used
to make the imaginary yellow energy-cost stickers.