The conquest of both Mexico and Peru--at least of the dominant Indian culture there--involved attacks by Spanish Conquistadores against established Indian civilizations who vastly outnumbered them. In both instances, the Spanish were cruel and barbarous, and destroyed cultures which in many respects were superior to the European culture of the time. In both instances, a tremendous number of treasures and artifacts were destroyed by zealous Catholic priests determined to wipe out any evidence of "idolatry."
Hernan Cortes led an expedition against the Aztec Indians of Mexico who were ruled by a priest/Emperor, Montezuma II. Cortes' blonde beard and blue eyes bore a striking resemblance to an Aztec God, Quetzalcoatl, whom the Aztecs believed would return from the sea. When the Spanish first arrived, Montezuma sent many gifts of jewels, gold, etc. to them in hopes that they would accept the gifts and leave. Of course, it had the opposite effect. When Cortes met Montezuma, he told him
We Spaniards have a disease of the heart which only gold can cure.
Cortes' men attacked the Aztec capital of Tenochtitlan but were beaten back. The Aztecs then killed Montezuma as he had not been able to prevent the attack. Cortes returned with other Indian tribes who allied with him (they hated the Aztecs as the Aztecs had kept them under cruel subjection and raided them for sacrificial victims.) The combined Spanish and Indian forces together with an outbreak of smallpox ultimately destroyed the Aztec civilization. Mexico City is built on the site of the Aztec capital.
Francisco Pizarro destroyed the Incan civilization in Peru in much the same fashion. At the time of his arrival, the Incan ruler, (known as the "Inca") Atahualpa, had just fought a civil war against his brothers. He was considered weak and ineffective. When Atahualpa and his entourage rode out to meet Pizarro, the latter had him seized and kidnapped. Pizarro then drew a chalk line in a room and agreed to free Atahualpa when the room was filled to the chalk mark with gold and silver. The Incas complied, but Pizarro went back on his word and had Atahualpa murdered. Pizarro's men then systematically destroyed the civilization and raided it of its wealth.
An excellent description of both civilizations and their ultimate destruction is found in Charles C. Mann's 1491. An older but very entertaining (in not totally accurate) account is in William H. Prescott's History of the Conquest of Mexico and History of the Conquest of Peru.
Maybe this question shoul be, "Compare the Aztec conquest of Mexico with the Inca conquest of Peru."