Could you clarify your question? It seems to read "Why are Asian Americans more accepted in American culture than Black Americans?" If this is what you are asking, then the premise itself is incorrect. Asian Americans, more than any other ethnic group, are regarded as "perpetual foreigners", and commonly are asked "Where are you REALLY from?"

Asian Americans have no where near as prominent of a position in American popular culture as African Americans. There is an entire industry which caters to African American movie and television audiences. Only in the past few years have we seen television shows which feature Asians as the dominant focus. Media also frequently gets away with ridiculing Asian Americans; there is virtually no outrage over the portrayal of Asians in Two Broke Girls; in contrast, see allegations of racism regarding Jar Jar Binks. Similarly, the The Airbender Movie scraped its Asian roots in favor of an entirely non-East Asian main cast.

If you are asking why Asian Americans do so well economically, then you are buying into the Model Minority Myth. This is perhaps the most harmful perception of Asian Americans, as it is not only false, but it establishes a "bamboo ceiling" and limits Asian American cooperation with other minorities, especially Hispanics and Blacks. Quotas are frequently placed on Asian American attendance to top universities. Amidst all of this, Southeast Asian populations, such as the Hmong, have up to 80% unemployment rates. This also highlights an innate racism which lumps all Asian Americans together, despite coming from diverse cultures and backgrounds, from a geographic area twice the size of Europe.