Spanish Conquistadors destroyed both civilizations.
Not just them, but any native American culture that was contacted by Europeans.
The Aztecs original name is "Mexica", I knew the origin of the term Aztec, I'll have to review my notes, but I do know it was a term accepted during the arrival of the Europeans.
Aztec and Inca
They wanted to capture the empires' gold and resources.
Both empires were relatively the same size. They were, however, marginalized in Peru with the arrival of the colonial Spaniards. Some say for every 1 Inca, there were 2-3 Aztecs.
Spain conquered the Inca and Aztec Empires. By the time of European arrival, the Mayan civilization had imploded four centuries prior.
Peaches were not traded in the Aztec capital city of Tenochtitlan, at least before the arrival of the Europeans.
Not just them, but any native American culture that was contacted by Europeans.
It pretty well destroyed the Aztec Empire, and enriched the Spanish.
The Aztec people of northern Mexico, arrived in Mesoamerica in the 1200s. They settled the city of Tenochtitlan and flourished in Mexico until the arrival of Europeans in the 15th century.
Assuming this question is asking about about trading items before the arrival of the Spaniards (or Cortes):The Aztec people did not have guns before the arrival of the Spaniards. Once the Spaniards arrived, the Aztecs traded their goods (gold, food, etc.) with the Spanish people for guns and gun powder.
The spanish conquered the Inca and Aztec empires in America.
The Aztecs original name is "Mexica", I knew the origin of the term Aztec, I'll have to review my notes, but I do know it was a term accepted during the arrival of the Europeans.
Spain
The Aztec and Mayan empires did.
Mexico
Aztec and Inca