Not that different. The basics of helicopter flight can be grasped through games such as Battlefield and Arma, and easily transferred to a sim such as BS.
I know helicopter flight models in games like BF are "arcadey" at best, Arma tries a little harder in my opinion, but I don't understand this common attitude that these are "nothing like" what you find in BS.
To answer the OP, as others have mentioned, check your axis assignments, as pushing forward on your stick should initiate forward movement.