We're not flying Spitfires and Messerschmidts in elite, so you don't have to get on their tail [haha]
I find one of the main advantages of FAoff is that you don't necessarily need to get on your opponents tail while both of you fly "forward" to shoot them; instead, because you have decoupled your vector (direction of travel) and your attitude (direction your ship is facing), you can fly in parallel to them at their side and keep your weapons pointing at the sides of their ship. Or, a much more basic FAoff tactic, is you can "reverski" (fly same direction then using FA off turn to face them, this is a very old, regarded as lame, but still fairly effective, tactic though.
If you imagine your opponents ship as having a 10-15° cone growing out of it denoting the area that its fixed and gimballed weapons can hit you in, that leaves you 345-350° of pitch & yaw around your target giving you nearly a complete sphere in which you can position your ship while keeping out of their weapons arcs of fire. This however, obviously doesnt apply to turrets. As long as your position is such that the direct line from their ship to yours is in this larger safe sphere rather than the narrow danger cone, you have an advantage. And if your ship is pointing in that direction of the direct line, regardless of what direction you are travelling in, you can fire on them. Using FAoff for combat creates more opportunities for those two things to line up making it easier to win engagements, however it does require more proficiency from the pilot.
There are many good guides to FAoff on youtube should you wish to develop those skills. After a while of flying FAoff it just feels oh so much more natural and satisfying, although I'd say I personally couldnt do it without six analogue axis' on my controller set up, I have next to no idea how the keyboard and mouse guys do FAoff. Although having said that, from other discussions I gather that relative mouse offers greater precision for aiming, so maybe it offers a similar advantage for FAoff?