I think I should probably qualify what I think Brown is going to be good for, and I am going to contrast it with double on half, simply becuz I do think that way.
I like brown because it's fitted on the whole piece, without giving up the symmetry of double on half.
Double on half is automatically symetrical whether the furniture is the same on right and left or not. The differences, if not perceptable to the eye, are genrally a non issue, provided you use cotton, no backing, the cotton has some weight and or body, and it's tweedy or it's busy. That will disguise your differences.
Brown takes over when the shortcomings of left and right sides cut the same ( though they are not ) are perceptable. Perception is key, you may be lazy like me and pretend you don't see it, or overly fearful and believe the differences are stark when nobody else would care.
Brown has pieces cut symetrically, and then fitted on the whole chair. You might choose brown ( or Karen's method, or Pat's or Janelles if RS out or Alicia's) so that the left and right are given equal due, but Brown gives you some tricks.
Brown lets you take some lazy ( my favorite ) shortcuts and chalk out, measure or trace for speed, and table cut those pieces so that you aren't bending, and then overlock and cord. Then, you get to assemble ( after pin fiitng double on half ) and overlock inside body pieces, and then the final fitting is seams facing you, so that you can hand them off to a unskilled person to sew. It's already corded, pinned in a single layer to sew, and RS out or WS out as you prefer.
Sorry, I gotta get psyched to get the creative juices flowing. Call me obsessive compulsive. THis will be what I dream about for a month.