The answer to this can be found in Chapter 18. Specifically, it can be found on pages 355 and 356 in the paperback edition of the book. As with much else in this book, the answer has to do with food production.
Over and over in this book, Diamond emphasizes the idea that food production makes societies powerful. He says that societies that get agriculture first have a longer time to build up their strength and are, therefore, typically the conquerors. This is the major difference between Eurasia and the Americas; Eurasia got food production long before the Americas did.
Diamond says that
The most glaring difference between American and Eurasian food production involved big domestic mammal species.
Diamond says that Eurasia had 13 species that could be domesticated. By contrast, the Americas only had one, and that mammal, the llama/alpaca, only lived in a very small area of the land mass. What this means is that people in the Americas did not have sources of animal protein such as meat and milk. They did not have anything to pull plows or provide manure for fertilizer. They did not have anything to pull carts to transport goods. All of this meant that people of the Americas could not get food production and develop their society as quickly as Eurasians could. To Diamond, this is the most glaring difference between the two land masses.