With FA off, the ship behaves according to Newton's law of inertia. This means any movement you start, will continue unless you counter-act. So, if you start a roll maneuver, the ship will keep rolling until you command another roll in the opposing direction. With FA off, you ship is more maneuverable, very useful for combat if used correctly. Used incorrectly, it can be disorienting and get you killed.
When you are flying with Flight Assist ON you will move only as long as there are inputs from pilot. That means if you pitch up you will move there but only as long as you keep that input and if you release the stick or stop pressing a key the ship will stop moving to that direction – ship's thrusters will automatically counter that with equivalent opposite force. This feels more like atmospheric flight.
You will have a blue sweetspot for maneuvering depending on how many pips are diverted to ENG (engines) and for faster turns always must keep the speed there (as seen in image below).
Benefits are easier to control your ship and you don't have to compensate your previous input.
When you are flying with Flight Assist OFF your ship will not counter anything you input but add that to current flying vector so you will move forever how you are moving now. You can fly in one direction and keep your nose in any other, also with Flight Assist OFF you can turn a little bit faster, that's why many pilot's right before making a turn toggle FA OFF.
There is no blue spot and your maximum speed is still capped to 500m/s, but you can do crazy stunts, like fly with full throttle ahead but facing backwards or sideways. Also it makes aligning your ship to station docking entrace easier as you need to fly somewhere near the entrance and turn your nose in right direction before you want to toggle FA ON and only then you will change flight vector.
The benefits: first is faster turning speed but the main benefit is when you boost and turn FA OFF you will maintain maximum speed indefinitely, so point your ship to desired target, boost and turn OFF FA (but don't touch any inputs or you will be adding those to your current flight path as well) and you will go there at maximum boost speed without overheating.
Also in a dogfight is harder to hit someone with FA OFF who do not fly in straight line, but it is also harder to hit others when you are flying FA OFF, gimballed weapons do help.