I have played a shit load of FPS and TPS titles over the past year and a half using the 360 controller. In games like Call of Duty, the aiming is very fluid as the frame rates and sensitivity are balanced. I rely on strafe shooting at times. It helps when you're using a Sniper scope and can't aim the reticule in a proper manner. A large number of console game allow auto-aim feature and that always tends to dumb down the level of your skills. Although, I admit I had to use this feature in Red Dead Redemption and Episodes from Liberty City, since aiming distant enemies proved to be very difficult in these games. Always relax your thumbs when using the analog sticks. Get the feel of the sensitivity in any game before you begin and adjust it to your convenience from the controls option. In Gears of War, cover and shoot mechanism plays a very important role. In a close combat, you can use your Lancer's melee attack and tear those Locust horde a new one. The sensitivity in the game was just perfect, from what I remember. Also I assume you are zooming in with your weapon, when you shoot. Blind fire is seldom useful. The more you play using the controller, the more you get used to it.
I still remember my first horrible experience using the controller for an FPS game on a console. It was BLACK on the PS2. Games back then didn't feature health re-generation and I wasn't very used to the PS2 controller, in terms of FPS or even TPS gaming. So I ditched the whole idea and moved on with other controller friendly games. But with the advent of the 360 controller and it's shooter friendly design, I don't think it gets any better than this. You'll do fine, just keep playing.