Well, there's a number of things you have to understand before I give an answer.
First, I am used to hearing live sound as I played the violin and piano as a kid, played in a children's orchestra, and restarted the piano again about 4 years ago. Live sound in my experience varies - a lot. Further, I do not consider myself a critical listener, and I am not a connoisseur of small differences. Generally speaking when someone points out a difference to me I can hear it, but it's usually not a big deal to me. In other words, I probably tolerate (ignore?) small differences in sound more than many (most?) audiophiles, and don't really differentiate readily between pieces of equipment.
I am not a bass freak, a detail freak, and don't give a damn about sound staging. The ONLY time in over 35 years of listening to hi fi systems I have ever had a "way ahead in sound quality" experience was the first time I heard Quad electrostatics, which I have owned since the 1980s.
BTW my first headphones were Stax SR-5s, which I still have. I have heard TOTL speakers like the Infinity IRS, Apogees, Musicos and Avant Gardes, among others, and none of them impressed me over the Quads the way the Quads impressed me over anything I had heard before.
More bass, more highs, louder, yes. Better, as in, more like live music? Meh.
Frankly I think there is a lot of hype in high end audio (or as someone called it, hind end audio), and reviewers make a living exaggerating differences.
Here's the thing - Quads were introduced in 1955, cost around $1800/pair when they were discontinued, and when they are demonstrated at Hi Fi shows in the 2010s, they still make top ten best sounding room lists. That says a lot about diminishing returns.
In my experience, nobody has broken the law of diminishing returns in audio, and nobody has ever produced a system that sounds like the real thing.
Especially true for headphones, since nobody has heard a real live orchestra in their head, or even around their head - no, sitting in an orchestra is NOTHING like listening to one on headphones. My definition of, "way ahead in sound quality" means that I can notice a difference in the first minute, without straining to hear a difference or stopping to analyze it, and that has only happened to me once, so you probably see where this is going.
One weird effect of the HE-1s was that for whatever reason the soloist on one piece of music I tried was located toward the back of my head, which I have not heard with any other headphone. Since nobody else has noticed this presumably it was unique to me or the way I was wearing the headphones.