Historically, FPS belong to PCs and KB+M. And historically, they have been designed around that kind of control, allowing for twitch-shooters given the quickness and precision that comes with mouse pointing.
On the other hand, it's perfectly possible to design an FPS from the ground up for analog controls. Case in exam: KZ2 or any other shooter that wants to give you heavy inertia in rotations, and moving away from the "camera on a stick" feel that comes with the quick, precise, abstract mouse controls.
Thus, I think that you should define what you mean with "better controls". If by better you mean easier, quicker, more precise at moving an aiming reticule across a view then obviously the mouse is better in that sense. Just like pointing with your eyesight would be even quicker, even more precise, even more abstract. And even worse at conveying weight, because it would basically allow for zero inertia of your body/weapon.
In the sense in which the controls, like the game mechanics, graphics, sounds, are trying to convey a peculiar feeling or experience, it all comes down to the game design. A properly designed game will make the best of any control method, and even bring out the unique positive points of it.