Any meaningful differences...

Can't remember if I had blue or black, preferred stepped,  natural and clean but sometimes 1 click is to low and 2 is too much, they also get dirty and need cleaning sometimes, installed a TKD and though it was a little sterile. No longer have the BAT but it had 99 step,  that was an awesome volume control.

So you think stepped attentuator is more detailed vs a little bit of veiling disguised as warmth for high quality pots?

I like stepped attenuator because I can matching resistors for perfect channel balance and alter logarithmic curve to my liking.