Analogue sticks can sense like 255 degrees of tilt on each axis (at least thats what the DS3 driver for my PC was detecting when I connected it), and dividing those two cm of movement you can on each axis into 255 levels is obviously going to make everything you do with it require a lot of precision. Mice can however have as high a resolution as 1600 dpi, and you also perform mouse aiming over far more than two cm per axis. This alone clearly shows that it is easier to perform more accurate aiming with a mouse.
I also find the way you aim with a mouse to be more intuitive. To me, it feels more direct, while on a stick it is more like telling the game "start moving aim in x direction at y speed until i stop telling you to".
Even if both methods of input are dependent on each players skill level with that sort of input, I can't imagine a stick user outmaneuvering a kb+mouse user, given the same level of physical aptitude in each player, the same amount of training with their preferred input method, and in a game that doesn't interpolate analogue stick input.
It's sort of like tiers in fighting games. A person playing a mid-tier character can still beat a person playing a high tier character, but chances are the person playing the mid tier character would have been even better with the high tier character, given the same amount of practice. In this case, the laws of physics put KB+mouse on a tier above analogue sticks.
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