It's a lot of speculation, but if the game is bottlenecked by single-thread performance, then X1 could have an advantage over PS4 because of the marginal clock speed improvement, assuming that the PS4 version is using GNMX which is more CPU intensive. The only other thing I could see is a bandwidth issue, where for some reason the ROPs are bandwidth starved, like if they have a memory contention issue that's plummeting the effective memory bandwidth. That seems unlikely, but X1 having some dedicated GPU memory with ESRAM may alleviate that bottleneck. That would hinge on the assumption that fog, foliage are fillrate limited. I don't know what the performance implication of the flashlight are.
Either way, I wouldn't read anything into it in terms of general system performance, because it's not the most highly-polished optimized AAA game out there. It would just be a couple explanations for this specific game.