Interesting. I think they are pretty close but I think my PoT's have a slight edge especially at 18v and the pots definitely have a little different taper. One of my PoT's has the non-higher gain mod so a little different response than the Dukes or the other Prince even if dialed it to sound as close as possible and I think consistent with the slightly different regular gain KoT. I would say the Dukes get pretty close, but we may just be more sensitive to the differences.
That said, one worry I have for the Brothers AM is that it will be more like the Duke and likely even further from the King because of the compromises in packing in all that functionality in a smaller package with SMD's and digital pots. For many people the compromises are likely worth it, but if you are sensitive to the DoT differences, the BAM may not work well for you either.