This statement is most definitely true. It is one of the most important points (if not the most important) that Diamond is trying to make in Guns, Germs, and Steel. The Old World (and specifically Eurasia), had a huge advantage in food production over the New World. This meant that the Old World could become much more developed by the 1500s and could dominate the rest of the world.
The main question that Diamond is trying to answer in Guns, Germs, and Steel is why Europeans were able to have so much more wealth and power than other people of the world. He was inspired to investigate the question when he was asked about it by Yali, a man from New Guinea. However, the question applies as much to the people of the New World as it does to New Guinea.
Diamond’s answer in this book is that the Old World became dominant because it had better food production. It had better food production for three major reasons. First, it had more species of plant that could be domesticated and which were useful for people. For example, Table 8.1 shows us that the area from the Fertile Crescent west to Europe had 33 of the 56 species of grass with the largest seeds. By contrast, all of the Americas had only 11. These were the species that could become grains for people to eat. Second, Eurasia has a long axis that runs from east to west while the Americas have a long axis that runs from north to south. This is important for food production because it allows crops to diffuse, or spread. Crops can move fairly easily from east to west (or vice versa) because climates tend to be similar in that direction. By contrast, if crops have to try to move on a north-south axis they will often fail because climates tend to change as you move along such an axis. Thus, crops could move fairly easily in Eurasia, making it easier for people there to farm. Finally, Eurasia had many more species of large animal that could be domesticated. For example, Table 9.2 tells us that Eurasia had 72 species that could possibly be domesticated while the Americas had only 24. Large animals that can be domesticated (things like cows and pigs) are good because they are a source of food. They are also good as a source of manure to help plants grow more quickly. Finally, some of them can be used to pull plows and help with farming.
For these reasons, this statement is true. The Old World had better food production. This helped it to dominate the rest of the world.