Eurogamer: Battlefield 1 running on PlayStation 4 Pro offers a tangible performance advantage over standard PS4 owners, potentially offering a gameplay advantage to PS4 Pro.
Update:

Update 1:
There are rumors that claim BF1's multiplayer on PS4 Pro has been downgraded after patch 1.04 since this artice was posted. I will update this thread if Eurogamer revisits.

Update 2:
Eurogamer: UPDATE 16/11/16 10:02am: We've seen reports and discussion of reduced performance on PlayStation 4 Pro since the introduction of patch 1.04 yesterday, leading to speculation that the Pro features are disabled in the new update. Temporal anti-aliasing has been been tweaked, but we can rule out the disabling of Pro enhancements as our data is taken from the game running the 1.04 update. We've also just re-ran a small section of campaign tests and see no obvious impact to performance.