For moving, a stick is better, but for turning, aiming, and rotating in general, a trackball is the way to go. Personally I hate aiming with a stick, in Goldeneye (the good one) it was alright because the controls were absolute, if you pushed the stick 1mm to the left, you'd aim 5 degrees to the left, push the stick a little further and you are now aimed 6 degrees to the left. The problem I have with modern console shooters is that the controls aren’t absolute, if you push the stick 1mm to the left, you keep aiming to the left, if you miss your target (or he moves) you can't just ease off the stick, you have to push it the other way to find the guy again. I know it doesn’t seem like much of a hassle, but if you have a controller with some dead space in the middle from wear and tear then it becomes fairly aggravating.
Also with a trackball you help solve the problem of sensitivity, many games are way too sensitive, making it hard to aim with precision, others aren’t sensitive enough, and even if you push the analogue stick all the way to one side, you still corner like a freight train. A trackball is nice because there is no limit to how far you can turn, if you aren’t turning fast enough, spin the ball faster.