In latin american history, there were many periods where foreigners tried to control the governmental systems of the native peoples. In what ways would a historian most directly compare the actions of early conquistadors and the american government's interventions into south american politics during the latter half of the 20th century?
The comparison between the late 20th century and the early 16th century is quite difficult to make. For earlier periods, there are individual cases (such as William Walker in Nicaragua in the 1850s) where so-called "filibusters" behaved almost exactly like conquistadors. They came from abroad with a small but well equipped military force, tried to overthrow the existing political structure. None of them were nearly so successful or enduring as the original Spanish conquest, but the behaviours and general strategy were not so different. In the early 20th century, the US more officially occupied many Central American and Caribbean nations, ostensibly in order to force the repayment of their bonds, but also to install US-friendly governments, force unequal treaties, and in one case, build a strategically and economically relevant canal through the Isthmus of Panama. This is the era of gunboat diplomacy and the Roosevelt Corollary of the Monroe Doctrine. But none of this very direct intervention is in the time period you asked about.
Post-WWII, the United States has made plenty of attempts to influence the government of Latin America ranging from subtle pressure to direct military and intelligence support for a coup d'etat, either in the style of Pinochet overthrowing Allende in Chile, or the Bay of Pigs invasion (See: John Coatsworth, "Liberalism and Big Sticks" for a good overview). However, it has refrained in basically all cases from either direct invasion with American troops or direct governance of any Latin American territories. Insofar as what the conquistadors did was show up with an army, use a combination of violence and manipulating local politics to establish control, then rule in perpetuity as the new colonial elite, this is not something that has happened anywhere since WWII.
If one were to try and draw similarities, I suppose one could say that supporting one friendly local faction against another rival faction by giving them the advantages of cutting-edge (literally, in the conquistators' case) weaponry and tactics is common between both eras. Otherwise, the ways in which the United States exercised its influence in the region is almost entirely distinct from how the conquistadors did it five hundred years ago. Indeed, many of the most important channels of US influence (intelligence, debt negotiations, trade negotiations, foreign investment, military advisers) were basically unknown or irrelevant at the time of conquest. Overall, I would be very hesitant to make this comparison at all.
Edit: It is worth noting that there are a few exceptions here: the invasions of Panama and Grenada, the intervention in the Dominican civil war in the 1960s, and the US occupation of Haiti in the 1990s. All of these were relatively brief interventions, and were justified to the world as humanitarian in nature. And, of course, the US never did stop governing Puerto Rico, which remains a US dependency today, though it was not acquired in the late 20th century.