One of our group a few years ago did a load of work figuring out ship base agility stats for thrusters and boosts etc. I have decided to do some further work on this and built up max speed setups for each ship and directly measure their accelerations and decelerations etc. And I was doing all of this FA-off, of course, to get direct un-interfered thruster responses from that damn computer 
And in my testing I thought, for the heck of it, to see if the old thoughts on FA-on being able to brake you quicker than FA-off....
TDLR: It doesn't and in my measurements is quite a bit slower braking you than FA-off.
Data was captured by videoing myself going from 0 to max speed in various ships and measuring the time frame throughout the process to get the accel/decel curve for each axis (fwd/rev, lateral, vertical) and measuring the max accel/decel for each. I also measured the total time taken from 0 to max and back again to get an average accel/decel. The video was measured down to the frame using video editing software I use for highspeed analysis for work.
I found that the FA slows you down in a couple of ways.
The first is that it restricts your max vertical, lateral and reverse speeds.
Reverse is restricted to 80% of max speed.
Lateral & Vertical speed is restricted to 60% of max speed.
Ouch!
Secondly when measuring the total time to go from 0 to max and back to zero it added time to achieve this...
for example in a max speed adder.
FA-off from 0 to max speed took - 10.4s
FA-off from max speed to 0 took - 10.5s
FA-on from o to max speed took - 11.7s : an extra 1.3s!!!
FA-on from max speed to 0 took - 12.9s : an extra 2.4s!!!
Now the max accel and decel was the same FA-off v FA-on but there was a change in the profile with FA-on where it seemed to take a lot longer to figure out if you were actually wanting to go/brake at full thrust...
So like I said in the title.
FA-on IS slowing you down!
And in my testing I thought, for the heck of it, to see if the old thoughts on FA-on being able to brake you quicker than FA-off....
TDLR: It doesn't and in my measurements is quite a bit slower braking you than FA-off.
Data was captured by videoing myself going from 0 to max speed in various ships and measuring the time frame throughout the process to get the accel/decel curve for each axis (fwd/rev, lateral, vertical) and measuring the max accel/decel for each. I also measured the total time taken from 0 to max and back again to get an average accel/decel. The video was measured down to the frame using video editing software I use for highspeed analysis for work.
I found that the FA slows you down in a couple of ways.
The first is that it restricts your max vertical, lateral and reverse speeds.
Reverse is restricted to 80% of max speed.
Lateral & Vertical speed is restricted to 60% of max speed.
Ouch!
Secondly when measuring the total time to go from 0 to max and back to zero it added time to achieve this...
for example in a max speed adder.
FA-off from 0 to max speed took - 10.4s
FA-off from max speed to 0 took - 10.5s
FA-on from o to max speed took - 11.7s : an extra 1.3s!!!
FA-on from max speed to 0 took - 12.9s : an extra 2.4s!!!
Now the max accel and decel was the same FA-off v FA-on but there was a change in the profile with FA-on where it seemed to take a lot longer to figure out if you were actually wanting to go/brake at full thrust...
So like I said in the title.
FA-on IS slowing you down!