There is no secret conspiracy of MS (who did not make Battlefield) using a contrast filter to improve performance (if the same object has to appear on screen, why would darker lighting change the the load on the hardware anyways?).
I also don't think Digital Foundry purposefully messed with any footage, they just did somehow end up using 2 devices with different settings.
My take from this, both games have the same contrast. Xbox One version is more jagged in areas than the PS4 version. For the most part, the game looks pretty much the same on both though. I don't think either said has anything to complain about, and will get the same experience. Battlefield is a game being developed for many platforms. I think the best hardware comparisons would be games that are XB1/PS4 only.