Now, both experiments have agreed to a precision high enough that current metrology best practices will not have to change.
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.
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.