The question is not whether to use FA-off in PvP but to what degree?
Basically nobody who is any good at PvP never uses FA-off - Cmdr PoaArctica cited earlier is not using 0% FA-off - but the proportion of time with FA-off varies from 100% (as exemplified by a number of SDC/GCI pilots) to less than 10% (as exemplified by @Morbad).
Yep.
FA On and FA Off are distinct modes with distinct advantages and disadvantages. Even if your FA Off aim is flawless, you cannot bypass the fact that deceleration (or negative acceleration relative to your current movement vector for the pedantic) is faster with FA On. Likewise, even if you have full analog control over all thruster axes, and can perform the sort of maneuvers traditionally associated with FA Off while FA is enabled, you cannot ignore the fact that FA Off allows one to exceed the normal velocity and rotational limits that FA On enforces, often with more efficient use of ENG pips, as well as providing somewhat faster positive acceleration.
I generally prefer to stay FA On when possible, as my control scheme favors it (I prefer my primary weapons to be fixed and I cannot personally compete with the FA OFF fixed aim, of the best mouse & keyboard CMDRs), but I can and do toggle it off when the intrinsic differences of the mode prove advantageous.
What exactly is the advantage/disadvantage of flight assist off?
This is a complex question that varies somewhat from vessel to vessel.
Basically, with FA off you lose the automatic stabilizing and counter thrust effect of your thrusters, but you lose many of the limitations imposed by them as well.
You can maintain the rotational and movement velocities applied at higher ENG pip values at lower values with FA Off and bleed velocity more slowly.
The downside is the lack of compensation that makes aiming more difficult, and reduced magnitude of negative acceleration which can make the ship more drifty.
And how do you even turn it off?
You need to bind a control (or look up the defaults) to flight assist, and set it to either toggle the mode or to turn FA off while held.
My ship feels more "wobbly" when silent running.
Silent running, in and of itself, should not change the movement properties of the ship.