The situations in these two areas were similar in a number of ways.
Economically, both areas were essentially colonial economies. That is, they were economies that were generally being used for the benefit of other countries. European countries (and the US) were essentially extracting wealth from these countries without benefiting them to any great degree. This came about in China, for example, through the Opium Wars and subsequent unequal treaties.
Politically and socially, these countries were very stratified. There were small elites at the top that ruled the countries. Below them were masses of poor peasants who had neither political power nor any social standing.
In these ways, the Latin American countries and China were fairly similar to one another during the 19th century.