This is pretty much the same story just roles are reversed. In Your Lie In April a young boy is forced to play the piano to ridiculous standards, meaning he has no freedom in life. He meets a girl who is terminally ill and enjoys everyday he can with her, falling in love with her in the process.
Diamond Dust is along the same lines with more plot line dealing with the terminal illness aspect. A young girl is forced to play the piano, again to ridiculous standards, and all she wants in life is to be free. She meets a guy who is free in life and falls in love.
Both are good in their own way, if you enjoy one odds are you will like the other.