I so empathize with your situation. I have three comments for your consideration, one more practical, the other two unconventional:
1) Does she have chores/responsibilities in the household? I have always heard/read that if children have responsibilities in the household and feel like they are contributing, that it helps their self-esteem. You can make her tasks something different from her sister but something that benefits everyone in the family, like setting the table each night, etc. Just something where she feels she is making a valuable contribution and that she is responsible for.
2) This one is going to sound crazy and very unconventional, but I have to tell you because it transformed me when I was 13. I felt really ugly, very down on myself, no self-confidence, etc. Now I don't believe we should hold our value in how we look on the outside, but because that was my biggest concern at the time, this is what my Mom told me to do and it worked like a charm. When she told me to do this, I thought she was crazy, but I had nothing to lose so I did it and it worked miraculously. She told me that every night, I should go to the mirror, look at myself, and say to myself "I am beautiful". It's very important to look at yourself while stating the words, and the words need to be said out loud. I know this sounds crazy, but I cannot emphasize how much I was transformed over one summer by doing this. It was so hard to do this at first, and initially it made me feel ridiculous, because I really didn't believe in what I was saying. But I have to tell you that this one simple thing gave me so much self-esteem, and it wasn't long before I felt normal and natural looking at myself and hearing myself say these words! I imagine this would work no matter what the issue was related to self-esteem. Could be looks, could be personality, whatever trait is desired, I believe this technique works. If you decide to try it, I would be curious to know your findings.
3) We have such a strong effect on the people around us but when our children have an issue, it can be hard for us as parents to feel good. One way you can really help your daughter is to only focus on her positive attributes. I don't mean you should be telling her what they are, I mean in quiet contemplation on your own, think about all of the wonderful traits she has. Focus on them, feel them, see her when she is at her best in your mind's eye. Never think about the negative stuff (easier said than done, I know. You may need to use your will to do this). If you do this on a regular basis, you will start to notice that her positive attributes become more pronounced and she will most likely start seeing this too, which will enhance her self-esteem. It's hard to imagine that we can have this effect on others but we do.
I hope you didn't find this advice to "out there", but I have seen great effects using these techniques on myself and my children. Feel free to contact me if you have questions. I truly hope you find something that will work for your daughter.