Sibling rivalry is at its worst when the younger child outshines the older sibling.
I teach two sisters who are preschoolers -- one is four and one is three. Today we played a find the alphabet game. Each time, the younger sister was quicker in locating the requested letter and when we cheered and clapped for her, the older sister became despondent and seemed depressed. Their mother is always present and we really try to encourage the older sister with cheers and words of comfort. Is it okay to continue competition between the two of them in that way?
Try doing activities that are not so competitive with the girls. You can continue to work on the letters of the alphabet without the cheers, but find things -- such as drawing -- at which both sisters can be successful. When you do work on academic activities, make sure that both girls feel good about what they are able to do.
You may also want to ask the librarian at your public library to help you find children's storybooks on individual differences and strengths. Read them to the girls when you are with them and discuss the fact that some people are good at some things and some people are good at others.