I could be wrong, but it had little to do with AMD and more to do with MS specifications.
The only difference between the graphic cores on the Xbox One and PS4 is that the PS4 uses newer DDR5 memory, while the xbox DDR3. Xbox tried to compensate for the slower memory by adding additional cache on die, however this takes up physical real estate, which forced them to use a couple less cores (in exchange for faster memory handling). To simply say one is faster/better than the other is a bit misleading.
The reason for this was that MS speculated that the new DDR5 memory would be in short supply and there would not be enough production to supply their manufacturing. Considering the PS4, if they both used it, they would have probably been correct.
So anyway you are only looking at the GPU aspect, put it is integrated with the CPU, that does include an increased amount of cache on the xbox side. I think it is a bit early to tell what real life difference it makes. Early comparisons say little to none. Given time maybe, of course by then MS may adapt their design.
I am unbiased in this as I am not buying either, at least not for some time...