I don't think Olga "copied" her sister's clothes. Once the grand duchesses became young women, they were allowed to choose their own wardrobe. Olga decided to co-ordinate her clothes with Tatiana. The girls often did dress identically, but sometimes they were also divided into pairs when it came to what to wear. Tatiana did actually have an interest in fashion and it's been remarked by nearly everybody who knew her that clothes always looked stunning on her.
As for Tatiana being the "leader", this was simply her character. One might think that it would be Olga who would be more like that, but it was actually her younger sister, which didn't appear to bother Olga at all and the two sisters were always very close and united. By her younger sisters and brother Tatiana earned the nickname "Governess" because she was always looking out for them and to them she probably did act like one, maybe even telling them how to make their beds or clean their rooms, and also how she was very good at taking care of them when they were ill. In a lot of photos you might be able to tell how Tatiana was always looking out for them, or having the sweet and tender attitude towards them like any older sister..
When Nikolai, Alix and Maria left for Ekaterinburg, the Empress left Tatiana in charge of the household, and for her and Olga to take care of their little brother. Whenever Alexei had his terrible attacks of haemophilia, in which Alix would sit with him the whole time and of course would get very tired and worn out by stress, Tatiana was always the one to take her place to take care of him and try to distract him from his pain by playing with him and talking to him.
Tatiana's deep caring for others, as well as her regal attitude as a princess, beauty, and also her kindness and sweet yet enigmatic character is pretty much what makes her a favourite of mine.
