True, there are no brands of Coticules, but the quarry has/had several veins and some are smoother than others.
I have a select coticule from the La Grosse Jaune vein that's a good all-round hone as well as a great smooth finisher on just water.
I also have one from the La Veinette vein and it's a fast cutter, but a very sharpish finisher.
Where the select LGJ coticule finishes buttery smooth, the La Veinette is giving a sharpish feel.
So, indeed, mileage may vary.
In between, I've also owned a second select coticule from the La Grise vein and it wasn't buttery smooth either.
So, yeah hit and miss sometimes.