I've thought about this a lot as I have gone back and forth between my fixed and geared bike this winter.

I've decided one can't make a one against the other comparison.

Generalizations:

On level ground where I can maintain my best cadence, the fixie's natural efficiency wins out.

On relatively short hills (less than a mile), even against the wind, the fixie's natural efficiency prevails.

On long hills, or if the combination of wind and hill force me below my optimum cadence, the geared bike prevails.

Given my seven mile commute, the fixie takes less energy than the geared bike, regardless of wind.

Going up to Mount Bachelor, a long, long climb against the wind, and I just can't do it on the fixie.

I hope this summer or the next to ride my fixie from Bend to Portland, through the Cascade Mountains, a trip of about 165 miles with a dynamic elevation range of about 2000 feet and some long, long hills.
In order to do it, I think I need to gear down from my normal 72" to 69" or even 66".

I think I can do the hills and wind around town because for the most part I can stay within my efficient cadence range and within my anaerobic capabilities.
Once it becomes truly aerobic, over a long enough period, I have to gear down or suffer or both.

Anyway, I think too many variables exist to make a truly valid generalization.

Under 15 miles, though, and given the local dynamic range of about 1000', and my fixie takes a lot less energy than my geared bike.

I see this on hills I share with geared bike riders.
Within a certain range and distance, I seem to have an advantage, and then it suddenly disappears and they go past me.
The threshold between anaerobic and aerobic, and cadence, seems to have something to do with it.

Apples and Oranges.