There is a much bigger difference than that. Movement of a mouse directly translates to orientation of the character. A controller stick translates to rate of change of orientation of the character.
This works because you can move a mouse, lift it up, and recentre it. You can't do that with a thumbstick or joystick. You did notice this fact, but you did not notice how this allows position control instead of velocity control (well, orientation vs. angular velocity to be more specific).
Interesting stuff about controller input versus mouse input for FPS games. I did not know that the controller’s “look” stick controls the rate of change of orientation of the character. That certainly explains why aiming with a controller is not nearly as precise as aiming with a mouse. In fact, in a console FPS, the best way to aim with a controller is by using the “move” stick rather than the “look” stick as doing so allows for much more precise aiming than using the “look” stick. If the “move” stick controls character position like the mouse does, that also would explain why this tactic works as well as it does.