I think you can easily see what is going on- in the old days they simply used the word 'efficiency' as in the JBL example I gave and later simply changed the word to sensitivity, which really isn't how it works and for the most part no-one cares.
In order to know when you are applying 1 watt, you have to measure the impedance of the speaker at the frequency at which the power is being applied and then to the math to determine what voltage to apply to know when you are at 1 watt. The sensitivity spec is much easier since you merely apply 2.83 volts- and this is part of the reason sensitivity has taken over (this is also why digital took over since its so much easier to use in the recording studio). FWIW, '2.83volts' might seem quite arbitrary to many reading this, but it makes more sense when you know the legacy (which is what we've been talking about) is 1 watt at 1 meter assuming an 8 ohm load.
In any event, when you are using a zero feedback tube amplifier the efficiency spec is more useful since the amp can't double power as the load impedance is halved.
One area where this can get particularly pesky is when the speaker employs dual woofers in parallel. In such a case, the midrange and tweeter have an 8 ohm impedance and efficiency that is 3dB higher than that of the woofers, but the dual woofers cause the voltage source amplifier (IOW, solid state amp) to put out twice as much power into that woofer array and so the woofers keep up with the rest of the drivers. But when you put a power source amplifier on that speaker, such as an SET, you'll find that the amp is not making enough power for the woofers and so the system will have less bass and will be tonally tilted towards the highs. Although its not likely to be used with an SET, the B&W 802 is a good example of a speaker like this and there are many more as high end audio is plagued with designs like it. They are no good for zero feedback tube amps and not great for tube amps employing feedback (which can allow them to act like a voltage source but instead of doubling power as impedance is halved they halve power as impedance is doubled; part of why tube amplifier power is so expensive) either. I don't think they do solid state amps any favors either- the last thing you want any amplifier to do is work hard for a living- it will make more distortion and that distortion will be audible as less detail, brighter and harsher.
If there was ever a reason to be suspicious of the sensitivity spec when it relates to SETs this is it!
So when you see a loudspeaker that has a 96dB sensitivity spec, do your due diligence; do the math and convert the sensitivity to efficiency by looking at the impedance of the speaker. If its 4 ohms subtract 3dB from the figure...(while 96dB might be barely usable with an SET, 93dB simply isn't unless you are nearfield in a smaller listening environment). If it has a dual woofer array and is '8 ohms compatible' be very suspicious- there is a very real chance it won't work as expected with an SET. In this way you'll get a better idea of whether the speaker is a candidate for your amp.
Now there is a lot of 'common wisdom' (which might be a type of oxymoron) that you get the speaker you love first and then the amp that drives it. But any SET user knows that isn't how it works. SET users feel that SETs are the kind of amp that really brings home the music, so for them they have chosen the amplifier first- now they have to sort out what speaker works. This is why knowing the difference between the sensitivity spec and the older efficiency spec is so important to them.
(And FWIW since our OTLs also do not use feedback, this is a topic that I've been dealing with literally for decades; back in the 1970s I realized that if the speaker demanded that the amp have feedback, there was a good chance it would never sound like real music. This was and is because most amps that can behave as voltage sources lack the required amount of feedback to sound right; when you don't have enough feedback there will be distortion added by the feedback itself through the process of bifurcation of the input signal when combined with the feedback at the feedback node in the amp. No solid state amp made in the 1980s and most of the 1990s or before ever had enough feedback which is why there is a tubes/solid state debate. insufficient feedback will cause the amp to sound bright and harsh; typical solid state complaints. IMO/IME this is why there are still tubes around for audiophiles.)