Using a joystick does take a bit of time to get used to, and I've seen plenty of first-timers experience the same problems that you did (hell, I probably experienced them myself, somewhere in the mists of the past). While a mouse will usually guarantee that extra degree of precision over a joystick, it is entirely possible to aim very accurately using a stick. The key to this is compensation. You mentioned noticing that you tend to slightly overshoot your targets while turning towards them. Try this next time: when your reticle is just about over your target, zero out your motion and give your stick a slight movement in the opposite direction; this will help you kill your turning motion and leave you aligned with your target. With practice, you'll find that, during a dogfight, you'll be able to constantly be moving your wrist in all directions, always striving to center the reticle over your target. Smooth, reserved motions are very important; the last thing you want to do is compensate by overcompensating in the opposite direction.