I think the versions might be using different AA. PS4 might have MSAA or something similar and xbox FXAA, cause xbox version, while some objects look better then PS4, the overall image appears to be more washed out to achieve it. Would make sense, as FXAA is less intensive.
DF does hint at d3 ps4 using different post processing AA.
In certain places, x1 version does seem to have less aliasing but at the expense of slightly blurrier image. But we're really splitting hairs here.