I've always stated that the source is more critical than the amp but since I never had a had the chance to compare the modded 727II (a really solid amp) with a BHSE I still cannot be sure about how significant the upgrade can be.
But I think a certain characteristic of the headphone will still be kept (for instance an O2 will have much better controlled bass and less dark but it will always be a bit dark compared to the others etc. etc.)
I agree that it is technically more advanced in preserving the details etc. but how our mind reacts to this kind type of presentation is a different thing - in my experience anyway.
What I (noticed only a few weeks ago, oddly) this that even if the SR Lambda is capable of resolving quite a bit above my HD250 Linear Mk1 headphones, sometimes with the latter my mind still manages to pick up detail that I didn't notice with the Stax as it revealed so much that it slightly shifted focus to different things. So in that regard I wouldn't necessary call the former a more detailed despite the fact that it would dominate on measurements and stuff.
Also, I think the slower pacing of the dynamic headphone may have a role in this and it doesn't hurt that it is sealed as well (if they re-consider developing a 4070-like headphone I think there would be a lot of demand for it)
It is very interesting and I think I think I couldn't live without either. Sometimes less equals more (and not just for older recordings)
So in my opinion all three types of transducers have their own places, but the electrostats are certainly still too under-appreciated compared to the other ones.
And that's because not only they are only produced by one small company (for the moment, I don't know how serious Sennheiser is going to be), it is not being marketed nearly as heavily as other products. Maybe some changes are going to happen under the new ownership, who knows.
So if you think about this being embedded in the pricing of other products, you are getting more for your money's worth by buying a Stax in this sense (especially with the headphones, if I remember right I read that their profit is mainly gained by the amps and not the headphones).
Just something to keep in mind, when the next "newest, best thing" is going to be introduced.