I can't imagine the result of the different methods will always be the same even if they are getting "close enough" now? It's an advance in measurements, as far as I understand, but measurements always have some range, and how can they know the ranges for different methods won't change as the experiments advance?

(forgive me if this is unnecessary review. hazard of message board communication)

My understanding is that up until now they've been using a reference kilogram (Si sphere or, for the watt balance, a reference object) to measure Planck's Constant.

Now that they are getting repeatable, converging results for Planck's constant they can turn the process around; define Planck's constant and then use the apparatus to generate a reference kilogram.

And so the beauty of it is that any sufficiently motivated team could assemble the equipment (either apparatus!) and manufacture a reference kilogram that would be just as good as anyone else's.

Unlike the present state of affairs, where no matter how hard anyone wants to try, they simply can't manufacture a reference kilogram better than the one in Paris.

You could say the same about multiple measurements using a single method. In the event that we do find the results by different methods diverging, that is a better situation to be in than having picked one method and not being aware that the results are drifting.

However, as the methods are based on very well-established physics, there is good reason to expect that, as more measurements are made and any discrepancies are investigated, the results will continue to converge.