Hit the nail on that one- I wondered and still have no answers.
Played with all the emulations on my K3.
Came to the conclusion, what matters is how do I like the sound...
and so it comes down to- personal preference.
For me, at 25wpm or less, I tend to favor the sound and feel of Curtis- er... well... Curtis version 6, or, V6, in K3 language.
Faster speeds, 30-40 wpm, I find version zero, or default Logikey V0, to work better for me.
No one I know, and no where I've read, has the answers to the question you pose. I've heard statements like, "...so tell your Curtis friends..." etc etc, which leads me to think that Curtis (I know he was a man, perhaps a 'founding father' type of electronic keyer circuitry), is favored by Old Timer types who prefer Curtis because they've been using it for so long... however, keep in mind, I find Curtis timing to be very pleasant, and have been using it for less than one year.