I can confirm this same issue is visible with CH Products Flightstick Pro + Win 7. This issue is only visible for me in X-movement axis (cyclic left/right in game) but not in Y-axis (cyclic forward/backward in game). At least the visual movement of the helicopter controller in cockpit looks to be the same for cyclic forward and -backward when using joystick or when using keyboard.

This issue is not related to actual joystick but is dependant on the game, since even if I bind my Joystick Y-axis into cyclic left/right, it still only has the movement range of around 50% compared to keyboard. This issue was not visible in Arma2. Please handle this with priority as it currently impairs all flying in Arma 3 with gamepads and joysticks.