I do it differently.
I 'hang' the top Double, if you know what i mean and then reverse it on the bottom Double.
This way, i find it easier to do up the Brace, as its already got all the pressure on the gate and you can take the Brace out under a fully Boarded Lift - for whatever reason and you wont need a flat Spanner to do so, as the Double is in theory upside down and your Scaffold Spanner should fit.
I dont think it make any difference what way a Brace goes, but this is how i like to do it.