I think there`s a little bit of a placebo effect at work here.
First and foremost, how far away from the screen are you? That will dictate the size of the screen.
Secondly, on the assumption that the resolution is the same between a 32" and 60" (all 1920x1080) and the game will consistently display at the same resolution (whether 720p or 1080p or what have you) then the movement of the character is going to be identical to the movement of the mouse or controller. The game works by a particular resolution, not how large the screen is. It has no idea (in most cases, in particular consoles) how physically large a display is. You move the mouse an inch, your FOV will change accordingly the same amount regardless of TV size. What you can see however, changes in scale of course. You`ll be able to better see something in the horizon in a large screen than in a small. Conversely, you can see more by moving your eyes less on a small screen, so your reaction time is cut, hence the perception of smaller screens being better suited for FPSs.
Lastly, you can adjust the sensitivity of movement to suit if you want.
That said, you can get an 11" screen and sit on top of it and get the same result if you were using a 32", five feet away or a 65", 10 feet away.