Following these steps removes the sync between the controller and your PS4, so you’ll need to pair them again the next time you fire up the newer console. It seems that the PS3 doesn’t fully support the DualShock 4 either, with users on the Reddit thread where the wireless support was first outed noting that games with SIXAXIS controls and rumble features don’t work quite right.
Prior to the latest firmware update, the DualShock 4 worked with the PS3 as a wired controller. Now you can cut the cord, provided you don’t want to play a game that relies on motion controls.