If you played Halo Reach in Xbox 360 and then in Xbox One you will notice that you have to get used with the new Xbox One controller, and you would think that Microsoft enhanced it (and it really did) but the adaptation of Halo Reach to it is not good.
Basically as you can see in the image of the link, in One you have to move more the joystick when you want to move the aim slowly compared with 360, but since is not well implemented you will mostly use the Joystick of One all the way to the direction you want and forget about moving it slowly, which you could do and control better in 360.
This is based in my observations, I don’t have any tools to confirm this, but from my experience this is somewhat what is happening, there could be even some differences in the Dead Zones as well but I am not sure.