Some days ago I was convinced that my problem was solved by a stick calibration.
But alas.
The reluctance to turn around depends very much on the wind condition. So when I did a calibration and tested with no wind ... I was happy. WXhen the wond came back I was unhappy.
So I tought maybe the stick was the culprit, so I set the remote in mode 3 and now the yaw was on the right stick and the porblem remained.
So I tought maybe the compass, so I calibrated and the problem remained.
So I tought I reset the sensitivity to the normal value of 0.twenty and the problem remained.
So I set the camera to 1080 50fps and the problem remained.
Maybe I am just looking too close at having a slow uninterrupted pan in 4K...
This is what I think is not normal : when I push the left stick in one or the other way the drone hesitates to rotate until I apply more and more  stick and then suddenly it goes around, compromising my slow pan.
The same left stick also commands up and down. And when I apply up, the P3 does'nt go smoothly, but I hear variations in prop sounds.

Wind will certainly effect your ability to make nice perfect pans. Are you saying your drone doesn't react to your stick movements from watching the phantom itself, or are you seeing jerky movements in your footage? Is it the image on your mobile device that appears not smooth? Is your phantom behaving differently than it has in the past? Just trying to understand what you are experiencing.

The variation in yaw is so subtle that I cannot see it on the drone itself.But on the screen I see that the rotation has slowed down and that I have to put more stick to continue the rotation.
You are so right that it could be the gimbal who is not following the drone., but the drone turns at a constant pace. It is only since a few weeks that this bothering me.
Airdata says this about rudder response times : different values between left and right turns may be caused by worn out or unbalanced props. A long response time could exist if the aircraft is working on leveling itself due to turbulence or winds.Ricardo are you an former Walkera flyer ??

I suggest you take a look at the settings in the EXP menu.  Default value is 4.0.  Lower values yield a slower ramp into the full motion.  That helps smooth the action.  Perhaps yours are set below 3.0?  I use between 3.0 and 3.5.  There are YouTubes that explains this further.

A while ago I did reset the expo values back to default. Now I applied 0.40 on the rudder and shorted the sticks a bit.
Today with absolutely no wind I must confess that a had no trouble. Airdata reports short rudder responses of 0.1 s, short of instant.
I have to admit that a strong wind can prevent the drone to smoothly pan into the wind.....Thanks for the helpers.