I'm not in a position to address any comparative dealing with South or Central America, but the issues associated with North America are well attested. For over three centuries (seventeenth through nineteenth), there was an international perception that the US (and Canada to a lesser extent) represented considerable opportunity for the newly arrived. Often this was over hyped, but the reputation for generic opportunity attracted people by the millions.

Specifically, the lure of free or cheap land attracted multitudes from land-poor Europe. The poor could dream of crossing the Atlantic and becoming farmers, something that they often viewed as impossible in their homelands. Until the US frontier was officially declared as closed in 1890, it was possible to journey west and obtain some fairly good land for little money. That fact attracted people and helped flush out the population, state by state in a band of settlement that moved decade by decade farther west.

A different but no-less important process occurred with the California Gold Rush. J.S. Holliday's classic study, "The World Rushed In" is aptly titled: international immigration brought hundreds of thousands to the Pacific shore. Not all made the fortune in gold they imagined, but most remained and helped built the state into an economic powerhouse of immigrants: if it were a nation, California would now represent the 9th richest economy in the world.

After 1849, the nation experienced a duel movement of people: the older East Coast moving west was augmented by a Pacific coast moving East. This rapidly filled the interior.

You ask, "why were Americans so 'hungry' for land?" Land represented opportunity, not just for those already in North America, but even more so for immigrants. It wasn't an American hunger - it was international, and that is what fueled the explosive expansion of population across the continent.