I owned AN/Es (HE Kit 3s - basically equivalent to the factory SpE HE) and TL-D1s together for several months and went back and forth between them often. I think I can speak to their differences pretty well.
The Tonians are significantly faster and more open-sounding - they have a way with microdynamic finesse, esp. with percussion, I have basically not heard exceeded. Spellbinding.
The AN/Es had significantly lower bass as well as quite a bit more midbass energy. I also thought timbre was slightly better. Although the Tonians are never, ever shouty, being completely smooth and balanced, perhaps the AN/Es hemp driver gave slightly better harmonic density.
Although I preferred the Tonians for jazz I felt the AN/E was the slightly more well-rounded speaker.
Then I realized neither was really ideal for my huge room