DualShock 4 on XSX polling rate

[Dectur]

I’d like to use a DualShock 4 (PS4) controller on the Xbox Series X. If I set the polling rate to 1000Hz on the Titan Two device, will the PS4 controller (the one I’m using) communicate at 1ms to the console? Or will it be 8ms since I used a Xbox controller to authenticate?

Also if 1000Hz (1ms) is possible, do I set both input/output at 1000Hz or just one of them?