The differences between Baba and Amir in adjusting to their new life in California are primarily those of age; Amir is beginning a new life of opportunity with his future ahead of him, while Baba is facing the end of his life, after having lived always in wealth, privilege, and security. The adjustment for Baba, therefore, is far more difficult. Once a powerful and respected man, Baba's life becomes one of poverty and the dirty, manual labor he must perform to support himself and his son. He has far more memories of his good life in Afghanistan than does Amir. Being older, the culture shock is greater for him, as well.
In contrast, Amir is relieved to leave memories of Kabul behind, especially those related to his betrayal of Hassan. He finds love, pursues an education, and fulfills his dreams of being a writer. Being young, he is still developing his personal identity and can more easily adapt to his new culture. He does not experience the loss of a well defined former identity as his father must endure.