You mean Cubans, Puerto Ricans and Dominicans? We would usually think of them as Latin American, though 
In any case, the three groups are very different - and generally do not like each other. Furthermore, there is a difference between the populations and home and in the US. In the US, of course, Cubans are the most Republican of all the Hispanic groups. In contrast, Puerto Ricans and Dominicans are very Democratic (just check out the voting patterns in East Harlem, for Puerto Ricans, and in Washington Heights, for Dominicans).
For that matter, other Latin Americans are not particularly fond of Cubans either, which makes sense considering that Spain pursued a rather explicit and aggressive "Make Cuba White Again"strategy in the 19th Century that populated Cuba with many European immigrants, who embraced the rigid norms that govern a racial caste system. Many Cuban-Americans are the descendants of this group.
It's not hard to find stories online about Cubans calling Central Americans and Mexicans "indios" as a pejorative insult and being very bigoted towards Blacks etc. For this reason, there is little love for Cuban-Americans, along with the more obvious reasons for lack of harmony: Cubans who would be considered "illegals" are embraced by the American government and all other groups, outside of Puerto Ricans, are not. While South Americans must go through various hurdles to live in America, Cubans do not, so even if wealthier Colombians and Venezuelans share social characteristics with Cubans, there is some animosity.
Note: I don't share these viewpoints regarding Cubans and think that, generally speaking, Latinos get along fine, particularly when they work together at firms that largely employ white Americans.
