This is what I'm thinking, too. The xb1s has a little bit more gpu-power but what seems to be the bottle-neck is the memory-bandwidth. The higher clock-rates of the gpu also improved the bandwidth of the esram, so that should be the big difference between xb1s and xb1. Also the xbox has the slightly faster cpu, so this could be why xb1 has a little better frames (at a little lower res). The one memory pool for PS4 could also explain the lower framerates. Battlefield is normally also a CPU intensive game. So if the cpu has more cycles on memory, the gpu has less available. This could be a limiting factor in optimizing for the PS4. If you optimise your title it can heavily use the CPU, it steals memory-bandwidth from the GPU and the GPU might have to wait for some cycles and can't be maxed out. On the other hand, if you max out the GPU you can't max out the CPU. at least in this scenario it might be possible.