Not with the analog stick. Have you seen Unreal Tournament 3 gameplay?
I need to aim quick, I need to aim precise, and at high speeds. While I'm jumping I might see someone aiming at me during the jump. If I would be on my computer, headshot immediatly, on the PS3 I would be lucky to shot in a radius around the person.
Increase sensitivity and I can at least move around quicker but aim worse. Decrease it and I won't be able to turn the screen to the enemy that's attacking me before I die.