AR
Without ggiving a definitive answer, it wil likely depend on the phase of flight and the mode of the autopliot/flight director.
On an ILS the response will be much quicker (in general) than tracking a radial.
It probably depends on the phase of flight and the Required Nav Accuracy. In the terminal area with a Required accuracy of <1nm the response wil likely be quicker than when in an area where it is 5nm!