One similarity between the two stories is that the narrator in each is a member of an extremely restrictive society.
Beka Lamb describes a girl who lives in Belize in the 1950s. She does not fit into her society because she is Creole. There is a strictly religious government, and no deviation is accepted. Beka ‘s future is limited. Fortunately, she is able to enter an essay contest and win a scholarship that allows her to flee her restrictive society.
The she went to the attic, mercifully empty, to sit down with the pencil and essay again. It wasn’t long before her mother came to order Beka’s immediate return downstairs. (p. 155)
Beka’s mother does not appreciate the effort she is making to get a better life. This is similar to David’s situation in The Chrysalids. David has a special ability too. Beka’s intelligence sets her apart, and David’s telepathic ability does the same.
But after that she went on to warn me very seriously not to mention it to anyone else; other people, as far as she knew, did not have such pictures in their heads... (ch 1)
David is also in a strictly religious society, and his ability is what allows him to escape it. He and the other telepaths are forced to flee, and then they are rescued by the telepathic Sealand people.
One of the main differences between the two books is that The Chrysalids is science fiction taking place at some point in the future, and Beka Lamb is historically accurate, describing Belize in the 1950's.