Both companies will walk along each of this person's chromosomes, and will tend to find that each stretch is found in all three reference populations, but is most likely from Europe. This would be expressed by Decode as a high chance, maybe 80-90%, that the stretch comes from Europe, and a smaller chance, maybe more like 5-10% apiece, that the stretch comes from Africa or Asia. Adding up all the stretches, you'll tend to get 80-90% European ancestry, and 5-10% African and Asian ancestry, each, for the Northern European -- this is consistent with the Decode chromosomal ancestry analyses of Northern Europeans that I've seen. This is a reasonable way to show the data.
The reasoning behind 23and Me's Ancestry Painting is, while it's true that each stretch is found all over the world, we know or are willing to assume that the stretch can only have come from /one/ population, and it chooses the most likely population. For our example Northern European, for just about every stretch along their genome, the single most likely origin will almost always be European, and would be expressed in final ancestry proportion estimates of about 100% European, and about 0% African and Asian.
This is how Ancestry Painting and Decode can end up with different total ancestry estimates for the same person.
So, even leaving aside the question of data quality, deCODE's claims regarding James Watson's ancestry are revealed to be a hoax. Watson's alleged complement of 16% "black genes" was compared to a figure (originating with Kari Stefansson, I believe) of "no more than 1%" for "most people of European descent" -- a number clearly not arrived at using deCODE's platform. In fact, deCODE's technique can be expected to give most if not all Europeans implausibly high readings of non-European ancestry.