I am a long time halo gamer, and just recently bought (and sold back) cod 4. I could not kill anyone in cod 4 for my life. Ironic that you have the opposite problem.
Anyway, here are some tips off of the top of my head to kill people.
1) Halo 3 relies heavily on motion sensor.
Get in the habit of looking at that until you see a red dot, then bring your eyes back to the actual game. Once you learn the levels, you will know exactly where people are with respect to you (i.e. below you, coming around the corner, above you, etc.). Once you know where they are, plan a strategy. Since they are looking at the motion sensor as well, trap them into coming towards you, then throw a grenade on the ground where they will eventually be. A few bullets will finish them off. That is probably what is happening to you when you play.
2) Crouch!
Crouching will make you invisible to other peoples' motion sensors. This gives you the element of surprise and a chance to strategize how to kill.
3) Always try to have a battle rifle.
The battle rifle or br is the best weapon in the game. 4 or 5 direct shots to the head will kill an opponent. It will take time to learn how to maneuver and jump around while aiming at an opponents head, but master this and you will be well on your way to dying less. Remember that there is a scope on the br, which will help kill enemies who are farther away.
Good luck and happy hunting!