I have read--and given what we know of Olga and Tatiana, think it true--that Tatiana tended to accept, whereas Olga tended to question. For example, notations exist in Tatiana's hand which are reiterations of Rasputin homilies. It is my opinion that Tatiana was a born pleaser and placater who accepted authority and status quo and had limited interest in anything beyond the immediate. She was bright, practical, efficient, and accomplished, but--in my opinion--without imagination. I would even question whether she fully explored that which she copied; I think she often wrote things down as a child might write, 50 times on the blackboard, something that had been ordered by the teacher.
Olga, on the other hand, was emotional and sometimes indiscreet, but also a critical thinker who, from childhood, took an interest in what we would call "The Big Picture." It is my opinion that whether the words she wrote were hers or transcribed from another source, she vetted them intellectually before committing them to paper.
Oddly enough, it seems Olga was closest to her father, who in my opinion was not much of a critical thinker. Tatiana, on the other hand, devoted herself unquestioningly to Alexandra, who admittedly had become rigid in her thinking but earlier in life had grappled with philosophical issues, not the least of which was whether she could morally, ethically and spiritually change religions in order to marry the man to whom she felt physically attracted.