Afro-Caribbean values, beliefs, and experiences will inevitably be different from Black Americans by virtue of their distinct backgrounds. Similarly, recent immigrant from Ireland will have a profoundly different view of the world than an Irish-American whose parents immigrated in the 19th century. The fact that American's obsession with physical 'racial' trappings elides the difference between native-born African-Americans and Afro-Caribbeans can cause great frictions within the Black community, as well as surprise such recent immigrants.
Afro-Caribbeans are a diverse people, as diverse as the many nations and tribes of Africa. One cannot proclaim if the have more in common with their Black or White American counterparts: even the transition of different African groups into American society is easier for some Africans, and more difficult for others. Class often has a greater influence upon the ability of various Afro-Caribbean groups to make an easy transition than nation of origin -- a poor Haitian may have more in common with both Black Americans and Whites of his class; an educated Kenyan may have more in common with Ivy League educated Black Americans. Regardless, the main difference between Afro-Caribbean immigrants and Black Americans is that the former have an 'immigrant' experience. They must make linguistic and cultural adjustments. They often enjoy group solidarity and tight-knit community support, than Black Americans may lack in many sections of the nation. However, both groups still face discrimination because they are characterized, in the racialized eyes of America as 'Black' and to address the social needs of these different groups, difference rather than racialized sameness is a more effective paradigm to apply when analyzing these both social categories.
Douglas A. McVay, "Race and prison," Drug War Facts, 2006, December 29, 2009, http://www.drugwarfacts.org/cms/node/64