I think that the major difference between Jing-mei and her mother is the their view of status. About halfway through the story, Jing-mei decides to be happy with who she is. She will not be forced into becoming something that she is not. She's happy how she is. Jing-mei's mother, on the other hand, wants to force Jing-mei into being a child prodigy of some kind. Part of her reason for pushing Jing-mei is so that Jing-mei can be can be famous. That would make Suyuan famous by association.
"If she had as much talent as she has temper, she'd be famous now."
Suyuan definitely believes that fame, fortune, and status is part of attaining the American Dream.
My mother believed you could be anything you wanted to be in America. . . You could become rich. You could become instantly famous.
I believe that is a key difference between the two characters. Suyuan feels this need to push herself and her family hard to achieve fame and fortune; however, Jing-mei doesn't see that as a worthwhile goal. It's not that Jing-mei is lazy. She simply doesn't feel an overwhelming need to mold herself into something else that might bring her fame and fortune. Jing-mei believes that her own identity and happiness is ultimately more important than fame and fortune.