You could turn up the sensitivity in windows... not sure if the in-game mouse sensitivity (F2 key) will change the menu responsiveness or not.
To be clear, this has nothing to do with sensitivity or the deadzone (the joystick deadzone slider affect the mouse, btw). The problem here is, thats its a entirely different type of mouse control than in FS.
Freespace mouse control was like an FPS: the movement of the mouse directly translated into an equivalent turn of the ship. That means if you dont move the mouse, the ship will not turn. This has two effects:
1) to contantly turn you also have to move the mouse constantly in the same direction. If you reach the end of the mousepad or any other obstacle you have to lift the mouse and set it on a convinient spot at the mousepad manually.
BUT 2) it provides an extremely high precision with the ships "nose" itself.
With this new control scheme your position of the mouse cursor on the screen determines the direction and turnspeed of your ship. Instead of directly controling the ship you only set the direction and speed of the movement. This means if you want to stop turning you have to position the mouse cursor back into the center of the screen. But unlike a joystick, which has itself a center it can "snap" back to, there is no guidance for the mouse. It is very easy to miss the center or shoot the cursor way over in the other direction. The effect is a massive loss in precision.