In the case of a noisy process value, what are the pros and cons of filtering the process value (PV) versus filtering the controller output (CO) or maybe both?

Filtering PV changes the process model and affects PID constants. I was told that ISA standard recommend not filtering the process value in a PID but I didn't find proof of it. By filtering PV you already have all in (constants for a given first order filter applied).

Thanks