This is a good question. Back home Baba was an important figure. More than that he had friends and things were familiar. People knew him, knew his family; he shared a common culture and ancestry with his neighbors. In a word, he had community and honor within it. In America, he was a nobody. Moreover, things and people were foreign. He felt alienated.
For Amir, America was completely different. It was an opportunity for him to grow, explore, and most of all escape the painful memory of his life in Afghanistan. So for Amir it was a nice start, a new lease on life. For Baba America was the death of a past he loved. The context of the words you quote above is an eloquent observation of the different perspectives.
I glanced at him across the table, his nails chipped and black with engine oil, his knuckles scraped, the smells of the gas station--dust, sweat, and gasoline--on his clothes. Baba was like the widower who remarries but can’t let go of his dead wife. He missed the sugarcane fields of Jalalabad and the gardens of Paghman. He missed people milling in and out of his house, missed walking down the bustling aisles of Shor Bazaar and greeting people who knew him and his father, knew his grandfather, people who shared ancestors with him, whose pasts intertwined with his. For me, America was a place to bury my memories.
For Baba, a place to mourn his.