This is an interesting thread about the sisters' relationship. As there were 8 years between them, I think that growing up Alix may very well have seen in her sister an authority figure or even a mother figure. Ella herself mentions this in a letter in "A Lifelong Passion," where she acknowledges hearing rumors that she was jealous of Alix being Empress, since she was just her little sister, and Ella basically writes that those allegations are ridiculous and that she was never jealous of her sister. She also writes that, on the contrary, because of their difference in ages, she always considered Alix almost like her child as well as her sister.
Once Alix was Empress, it seems that Ella definitely respected her position and was eager to be in her good graces. Ella was actually said to have been quite ambitious, probably due in part to the influence of her husband Serge. The couple were enthusiastic about having Alix marry Nicky, and they greatly encouraged their relationship. No doubt the thought of having her sister as Empress, and all the attending benefits, would have appealed greatly to Ella. Nicky confided a great deal in his "aunt Ella" during his courtship, and she was ultimately the one who convinced Alix to marry him by calming her fears of converting. I have also read that there was a time when Ella and Serge felt their influence on the young couple was waning, and it was at this time that they played into Nicholas's anti-Semitism by recommending to him an anti-Semitic book that Nicholas liked very much and commended them for, which I believe was called "The Protocols of the Elders of Zion." Some claim they did this deliberately to play into the Tsar's fears and natural aversion to the Jews, and thus gain favour with and influence him again.
Overall, I think Alix and Ella had a generally close relationship throughout their lives, and this turned sour at the end, when Ella was vocally opposed to Alexandra's dealings with Rasputin. The last time they saw each other they left on a sour note. However, I remember that Ella sent her sister treats such as chocolate and coffee when she was imprisoned in Tobolsk, and Alix gladly accepted the gift, so perhaps they didn't hold a grudge against each other for too long.