That's a question with no clear answer, that I can find. It also shines some light on a little acknowledged knowledge gap in the bigger subject of building heating and cooling, which is substantially based on affording air heating and cooling more weight than the other heat transfer dynamics.
Heat is transferred in three different ways; conduction, convection and radiation. For some reason, most of our attention is on air and conduction, which has resulted in a pair of "common sense facts" - that 'heat rises' and that insulation works by 'trapping air'. But these two facts are only true about air... hot air rises and air is a good insulator, unless it is moving. But air is worthless when it comes to impeding radiant heat transfer.
Our skin senses heat and cool, and it tracks both through radiance and conduction. But it may be more sensitive to radiation - think of sitting in the shade with an air temperature of 50 degrees vs sitting in the sun at 50 degrees. In the first case you would be cold, the second you would be comfortable (in the absence of a breeze).
A Rumford fireplace works on the principle of radiant heat transfer, not the heating of air. It is known that buildings with radiant heating systems will be comfortable at air temperatures of 5-10 degrees lower air temperature. Radiant heat also heats up objects, which then both re-radiate heat and heat air. Radiation moves equally in all directions (until something is in its path), unlike heated air, which rises (the ceiling zone is warmer than the floor zone).
Wood stoves often heat both air and radiate heat, though they are known best for standing next to on cold days to get warm fast (that would be the radiant component at work).
Given these characteristics, it could be said that radiation is a more efficient means of heat transfer than air, though our basic methods for evaluating heat efficiency (and heat loss, btw) primarily measure air heat transfer. Heating appliances, like a gas boiler, can have their fuel conversion efficiency measured, but that sheds little light on their end use heating efficiency. All of the data I could find in a 20 minute internet search was about appliance fuel conversion efficiency.
The only way to evaluate comparative building heat efficiency would be to conduct complete building system monitoring of the same structure using different heating appliances. I don't think that has been done to compare fireplaces to furnaces to boilers - of course, the heat delivery system variables would also need to be tracked. Pretty complicated.
That didn't answer your question, but I hope it was interesting. Incidentally, I did read that most
fireplaces are positive contributors to space heating. I was under the impression that most are negative.http://www.rumford.com/articleRumford.html