Filtering process value (PV) or controller output (CO)?
First, fixing up your process value measurement is always better, assuming that it's a noisy measurement and that the value itself isn't bouncing around.
If the PID controller is a linear device, then -- aside from what the controller &quot;thinks&quot; is happening -- there's absolutely no difference between filtering the input or filtering the output.  That's because if you have two perfectly linear systems (i.e., your filter and your controller), the order of filtering doesn't matter.
If your PID controller has no monitoring*, then the only difference between filtering the input and filtering the output is how it affects the controller nonlinearities.
I'm trying to think of cases, and in all of them it's seeming to me like filtering the process value is better.  You'll be less likely to hit limits within the controller for both the proportional and differential actions, and there's some styles of integrator anti-windup that could be &quot;pumped&quot; by excessive noise, partially or entirely disabling your integrator action.
* I'm not going to comment on monitoring beyond this, because I don't know what's done in industry.