Stax amplifier vs Stax adaptor

I’m wanting to know what the difference in sound quality would be between a Stax amplifier and a Stax adaptor. The Stax seem to run happily on just a few watts, from a set amp with an adaptor. I’ve never tried a Electrostatic amplifier, nor do I understand how one works. The after market of an adaptor seems to be minimal, while a used Electrostatic amp seems to command substantially more. 
Although I've never used an adapter I'd expect that the difference would be dependent to a significant degree on the specific Stax amplifier and on the specific power amplifier that is being used with the adapter.

Over the years I've driven my Stax Lambda Pro headphones with a solid state Stax SRM-1 MkII amplifier, with and without a Stax ED-1 "Diffuse Field Equalizer," as well as with a tube-based Stax SRM-T1 amplifier. (All of these products date from the 1980s). By far the best sound quality was with the tube-based SRM-T1, which I continue to use after selling the other products some years ago. The SRM-1 MkII was quite disappointing in comparison with the SRM-T1, as was the SRM-1 MkII + ED-1 combo. Although on the majority of recordings the latter combo was preferable to the SRM-1 MkII alone.

-- Al  
Although I totally agree with Al's assessment and experience, as I had the same ( I no longer own any of these Stax products ), I would like to add one more thing, which I am not sure Al " completely " answered, based on the entire question. The passive adapter was, an aluminum box, with a switch, a resistor or two, and some basic wiring and jacks, which was nowhere as expensive as the amplifiers Stax offered, nor, as Al stated, not as good, ultimately, as the Stax tube driven amp. I tried many amplifiers with the passive box, and found it to be an excellent way to " listen " to qualitative differences of amplifiers, although, unfortunately, never found the Stax phones to be comfortable, for long term listening. As far as history, Stax has been around for a very long time, have developed amplifiers and speakers,  and, are still in business today, catering to the ear speaker community. Enjoy ! MrD.
Interestingly, I followed the same path as “almarg.” I bought a pair of Stax Lambda Pro headphones in 1990, powered by the Stax SRM-1, Mark 2 (with the ED-1 equalizer). At some point, I sold all that and upgraded to Lambda Signatures, with a Stax SRM-T1S. Since then I bought a pair of Stax 009s. I saw an SRM-T1 here on Audiogon, so I bought it as a spare. I’ll skip all the audiophile description of the sound except to say that the SRM-T1 and T1S are far superior to the sound through the SRM-1, Mark 2. The only difference between the T1 and the T1S, is that the S has a balanced input, which I use.
I haven’t yet gotten myself an SRM-T1 for my Lambda Pros (still using the SRM-1 Mk.2. Hey, it’s not THAT bad ;-), but in addition their great sound the Lambda’s are also usually comfortable, unlike some earlier Staxes.
I still have  my Lambda Pro headphones and SRM-1 Mk 2.

Use them when my neighbors complain about my 2 channel stereo. 

Classical CDs only via Bryston spinner and preamp.