Good question. Maby its based on their personality as a human before they become a vampire. Like Edward couldnt read Bellas mind, it was kinda like a sheild. Now Bella's power is a sheild as a vampire.
Their superpowers are based on their different attributes they had in their human lives. For example, Edward must have been very intelligent in his human life, able to get inside people's head and know what they were thinking through wits alone. He must have also been very mwepesi, teleka as a human because he is the fastest runner of the Cullen family. Alice must have often had deja vu feelings, au odd forebodings that caused her to see the future in her vampire life. Jasper must have been very enigmatic in his human life, able to read people's facial expressions and moods au "auras," as I suppose wewe could call them. With the exception of Renesmee, she inherited her gift because her father, Edward, possessed a gift. Her gift is the exact opposite of her father's, the ability to send her thoughts to another with her touch. Bella, however, is a bit zaidi complicate and confusing. It says in the vitabu that Bella was sort of "destined" to become a vampire. It was her "fate," somehow. Her power is a shield. The fact that she was destined to be a vampire explains why her shield worked on Edward even before she was changed. He couldn't read her mind. Also, Bella skipped her ravenous newborn phase that most other Wanyonya damu are forced to go through for the first few years that they are a vampire. I believe that she gained the power to skip her newborn phase because of her maturity that she showed as a human. Her maturity shows often when she talks about helping her mother while she was in Arizona.