PC: i5-3570k, 16GB ram, GTX 970, SSD

Problem: the game starts to stutter hard whenever I connect my Dualshock 4 (PS4 gamepad) to play it.
Doesn't matter if it's by Bluetooth or USB cable.
Also it doesn't matter if I'm in the menus or in the game world.

An interesting aspect: if I alt-tab to another window, the game is smooth even with the DS4 connected.

This did not happen in the beta, I was able to play with the same gamepad.

The issue does not occur with XBOX 360 gamepad.