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. 

Hi fi fan seems you are expert DIY. Stock to stock do you notice huge difference  in transparency. For example top Primaluna preamps use Alps bluevelvet & some manufacturers  use stepped  attenuation  like Bat cj etc...

To some extent, it depends on the resistors you choose. I use nude Vishays (VAR series) in all my controls, and I never use a ladder - prefer one resistor for each value step of the control. Rotary switch by Seiden SG. Makes the total pricey - 20x the price - but worth it on first class gear, like my DIY phono/pre.

But - I suspect that almost any rotary switch and almost any set of decent resistors will surpass the garden variety volume control in transparency and warmth i.e. lack of distortion. But be aware that there are those who don't believe that resistors make a difference. Even experts.

I suggest that you try it out - find the volume that you usually use, and determine the associated resistance - and install several types of resistor of that value in a rotary switch. Then make an informed choice.

I did that experiment with a Seiden SG, and found Vishay VAR to be best for me.