I asked about this when my 15ohm Falcons needed less power than my 6ohm Harbeths with both having the same efficiency rating. BTW, I was using tube amps!
Ralph Karsten ( ATMA-SPHERE fame) gave a full explanation!
atmasphere
These days sensitivity (2.83V/1 meter) is how speakers are measured. There was a time when efficiency (1 Watt/1 meter) was the spec instead- back when tubes were King.
2.83 Volts into 8 Ohms is 1 Watt. That is why the seemingly arbitrary number.
When you cut the impedance in half to 4 Ohms, 2.83 Volts is now 2 Watts (which is a 3dB increase). So the impedance makes a difference! You have one speaker that is 6 Ohms and the other is 15. If the sensitivity is the same, for each doubling of impedance the efficiency is increased. So by my calculations the 15 Ohm speakers should sound about 4.5dB louder because they are 4.5dB more efficient.
When you are talking tube amps, because they can’t double power as impedance is halved (like many solid state amps do) the efficiency spec is more important. That means you have to derive it from the sensitivity spec and the impedance of the speaker. How I arrived at my numbers above is 6 is halfway between 8 and 4 Ohms so that’s a matter of 1.5 dB instead of 3 dB (which it would be if the 6 Ohm speaker were 4 instead).
The difference between 8 and 16 Ohms is its doubled, meaning another 3dB difference. I added the 1.5 to 3 dB to get my answer. Its not quite right since the speaker is really 15 Ohms, but its close enough for government work.