Girl mode is non canon, and thus adds nothing to the story.
Like I said, it's all non canon though since Persona 4: Arena confirms the protagonist to be male. Thus all of this extra character development amounts to nothing in the end.
FES is the ideal version since it includes The Answer, which Arena also confirms to be canon. So basically you're trading canon plot and major story details, for a non canon fantasy scenario. Not an equal trade off in my book.