I was comparing black bars to stretched, I wasn't talking about cm/ 360.
The sensitivity doesn't change and it won't change unless you modify your yaw/ pitch values. It appears to be faster due to the stretch in pixels.
If you could draw a circle on a 16:9 res, the same motion would make it look oval on 4:3, does your sensitivity change ? no;. If you want to convert from 16:9 to 4:3 use 0% mm that way it will feel right.
If he plays 4:3 his FOV would be 73.7398. stretch that on a 16:9 monitor.. its still 73.7398.