Apparently, Hanger 13 (the developers of Mafia ΙΙΙ) have been really sneaky with their patches. In a not so recent update, patch 1.05, the devs released not only custom rides and racing, but a PS4 Pro update that no one noticed.
This patch was added back in December and was first noticed a few days ago by Digital Foundry, which bumped the resolution on the Pro to 1440p on 4k televisions. It added along with it other visual improvements, like motion blur and improved shadows.
If you do not have a 4k television, you will still see some slight improvement even with a 1080p tv. Cutscenes will downgraded, because the game will run the launch assets of the PS4. Framerate should stay at a consistent 30 frames, but could drop at times but not below 25 FPS, and only during extreme moments in the game.
Check out a video below by Digital Foundry: