“Pizarro and Cortes...had armies of oppressed vassal states eager to overthrow their masters.”
That plus lances, armor and horses; especially horses. Time and again during the conquest, the Inca struggled to deal with the horsemen, they dug pits and set traps, but failed every time. The Spaniards were great lancemen.
read the book “1491” or other new books on the Americas before all the european diseases wiped out a lot of the population.
Both the Aztecs and the Incas were fairly new empires, who took over the land from other tribes who had lived there for centuries.