On paper, the PlayStation 4 does have a noticeable performance advantage over the Xbox One thanks to a higher-end GPU, and faster RAM. That advantage has been downplayed by certain vendors, but AMD states that it is greater than most people expect due to a certain hardware feature called hUMA that is exclusive to the PS4.
Senior Product Marketing Manager at AMD, Marc Diana explained at Gamescom that the PlayStation 4 comes exclusively equipped with heterogeneous Uniform Memory Access (hUMA). With hUMA, the CPU and GPU – which are already on the same die – have direct access to the same, shared memory pool. Both CPU and GPU can work with the same data without requiring programs to copy data back and forth between the two for maintaining coherency.
Older consoles, and presumably the Xbox One, may physically use the same memory chips, but CPU and GPU data is stored in distinct parts; you still have to copy data back and forth if you wanted to use both processing units side-by-side which is an expensive, performance-hindering operation.
Again, as we have explained numerous times before: this will not effect cross-platform games released in the earlier years of both consoles. We will only see the fruits of such hardware design decisions in the later half, that too on exclusive games.
It is not known at this time how many developers have committed to utilizing hUMA in their code.