Echoing what Robert Nichols said:

I'm in the midst of optimizing a brand new, Bryant 80% forced air, 2
stage, 110k Btu furnace. It sucks every BTU out of things when running
in the low fire mode. On high fire it is just trying to get you
comfortable enough to let it get back to the economy mode. I doubt that
the difference is more than a few percent but I suspect it is
measurable. If nothing else, the high fire mode requires the high speed
fan and attendant increase in electrical use.

Jon Elson wrote:
Pete C. wrote:

No, it isn't. It was documented on a well monitored high efficiency
model home where the backup heat strips on the high efficiency heat pump
were kicking in in order to provide a reasonable temp recovery time
since the heat pump itself did not have the capacity. The electricity
used during the temp recovery was more than would have been used on temp
maintenance due to the switch to lower efficiency backup (100% vs.
300%+).

OK, this is a killer example, where the furnace efficiency goes down the
tubes when it needs to raise the temp suddenly. It might be possible to
stage the temp rise to avoid that with a suitable thermostat.

But, many other heating systems have no such penalty for a rise in temp
setting, such as a traditional gas forced-air furnace.

Jon