Spanish colonies were divided into various Viceroyalties that were discouraged from having economic or diplomatic relationships with each other, while Portugal kept Brazil as a single unified colony. Even within these Viceroyalties, political rule was administered on a local level. Bolivar, in his brief presidency of Gran Colombia, attempted to centralize rule but this ran against already deep-set traditions of localism. In contrast, Brazil came to independence with a Portuguese monarch at its head, essentially retaining many of the colonial structures.

I do not know enough of Spanish colonial history to know why those colonies fragmented, but I can shed some light on why Portuguese America (Brazil) didn't.

In 1807, Imperial French and Spanish forces invaded Portugal. Rather than be deposed, the prince regent John VI, the Royal family and the rest of the Portuguese court transfered to Rio de Janeiro, Brazil, which became the capital of the Portuguese empire. There, João ordered, among other things, the construction of manufactories, the opening of ports to friendly nations (mainly the United Kingdom), the establishment of the Bank of Brazil and the creation of a military academy. As a result, in 1815 Brazil was elevated to a kingdom, creating the United Kingdom of Portugal, Brazil and the Algarves.

In the Portuguese mainland however, people started to revolt as a result of the absence of the king and the economic indepedence of Brazil. This forced João VI to return to Portugal along with the rest of the Royal family, leaving, however, his heir apparent Dom Pedro in Rio de Janeiro as prince regent. Having been raised up in Brazil, Pedro identified more as a Brazilian than a Portuguese. Thus, when the Portuguese tried to demote Brazil again to colony status, Pedro declared independence as Emperor Pedro I of the Empire of Brazil. A somewhat liberal constitution was made and a relatively bloodless war of independece was fought.

There were some separatist movements, however all but one failed. The one success was the province of Cisplatina, now Uruguay, captured during the Napoleonic wars from Spain. As the elites of São Paulo, Minas Gerais and Rio de Janeiro, the most powerful provinces, approved the Emperor, it was easy to subjugate the outlying regions and centralize the Empire. Many republican revolts would happen in the until the 1840s, but all were eventually subjugated.

follow-up question: Were there any Portuguese colonies in any of the Caribbean Islands, during the 18th century?