I have included a link from my notes, I have not actually tested it much beyond seeing that the gyro does work in steams "configure controller" thing, never got around to correctly mapping any game.
Some games support gyro directly, but even then AFAIK people prefer Steam Input due to how configurable it is.
With gyro you have 1:1 proportional camera position input, like with mice.
It's more or less about possibility of developing muscle memory. With (linear) gyro/mice you could sharply snap camera to a point you see on screen without much overshoot. You could turn 180 degrees in split second with eyes closed (actually with gyro people often use flick stick for such big rotations, turning instantly -- but that's besides the point)
With controller stick? Well you could try to time that 180 turn takes 1.5 seconds of holding at full deflection -- good luck developing a feeling for all the speeds inbetween zero and full deflection.
I guess I just need to try it some more.
I guess you've used some strange gyro to stick emulation (never heard of such thing, but sounds like it).
https://youtu.be/CiSS5OsNCNU from the creator explains it (and older gyro controls).