The situation is complicated there because in many countries a majority of the population is descended from both the conquerors and the conquered. They are a mixture of European and native (with ancestry from African slaves in many cases as well). Some people of mixed heritage identify more with the native side, others with the Spanish. People with more European heritage often make up the upper classes, while people with darker skin are often poorer.
The surviving indigenous peoples, who still speak their native languages, are generally very poor and discriminated against and there often remains strong resentment because of dominance by descendants of the Spanish.
The best relationship I can think of is between New Zealanders of European heritage and the native Maori. While there may be some resentment among the Maori over the fact that they are a minority in their own land and often economically disadvantaged, the relationship is not as bad as in other former colonial countries.