My two pet peeves with console FPS:
1) having to hold and wait while turning at a pre-defined maximum speed instead of just flipping around as fast as you can flick.
2) having to hold the stick on target and CONSTANT fighting with the auto return to zero/center feature, or having to rely on auto aim or aim helper functions in console games to compensate for this problem. Especially annoying when you have to contort your hands holding the sticks aiming up into the sky and to one side and you keep over/undershooting fighting with the auto center trying to aim you back down at the ground.
FWIW I always preferred touch pads and always hated those little eraser stick things too. I need linear 1:1 position relative control with pixel precision, not pressure based, and I can't stand acceleration built in to compensate for limited range of motion.