I have no experience of the xbox controller but having played this game with a couple of gamepads and having now settled (happily) on my PS2 controller, there are numerous things you can change in-game to help you out.
Go to the controller options and select the "advanced" button at the bottom.
I have the steering sensitivity set at 0%, deadzone set at 9% and speed-sensitive steering set at 90%
Try something like that and see how you get on. It should be obvious what changing these does but if you're not sure, let me know.