Another thing to point out: the American staple of maize is very nearly a complete provider of essential nutrients (just add beans), which cannot be said for Eurasian crops. And maize is the highest caloric yield crop, followed by potatoes. As 1491 points out, when the Mesoamericans faced the Spaniards, the Spaniards were probably suffering from lifelong malnutrition... and the Aztecs weren't.
The evidence is, in fact, that Mesoamerica in particular won the agricultural lottery, meaning that Eurasian supremacy cannot be based on agricultural superiority.