When I play shooters on PC, no I don't use auto-aim. For consoles, I have the feature on. This is because all thumbsticks have a "dead-zone".
What I mean by "dead-zone" is that little small area around where the thumbstick resets to when you release your thumb from it which doesn't have sensitivity. That dead-zone is detrimental to me, because sometimes I need that little tiny bit of movement to get a shot. When the thumbstick is moved out of that area, it's suddenly too much movement.
Regardless of your resolution; sometimes I need to turn this much to get a shot: I I. Thumbsticks don't give me that ability.
I also need to release the thumbstick before the crosshairs line up with my target, because information is still being sent until the thumbstick returns to the centre. It's something I haven't gotten used to, even after playing CoD4 on the PS3 since it's release.
On the plus side, the thumbstick lets me turn continuously, and move at a variety of speeds. Though I can adjust the sensitivity of the mouse, I can only move the mouse as much as my wrist, mousepad, or surface allows me. With the keyboard, I only have the option to stop, walk, jog, or sprint. With the thumbstick, I can move at 1 to 100% of the jogging speed; it's useful for those times when I want to peak around corners, or crawl through the grass undetected.