If you change the aspect ratio with black bars, say CSGO from 16:9 to 4:3 with black bars on the side, the sensitivity will essentially be exactly the same except you don't actually see what would be where the black bars are.
However if you stretch 4:3 to 16:9, the apparent sensitivity (i.e. aiming at an object you see on your monitor) will be different, even though the 360 distance is still the same. So it will feel faster, as you cover more monitor distance for each count the mouse sends.