There are a number of strong similarities between Mesoamerica and the Fertile Crescent. Both saw the development of advanced civilizations with large cities and road systems. In many respects, Mesoamerican culture was superior to that of Mesopotamia. Incas were performing brain surgery long before the practice was developed in Europe. Incas also learned to drill very small holes in stones to join them together long before this was developed in Mesopotamia. Both were agricultural societies, however Mesoamerica did not rely on rivers as was the case in the fertile crescent.
Aside from large work animals, two factors distinguish Mesoamerica from Mesopotamia. The people of Mesoamerica never developed the use of the wheel or the use of metals. They remained in the stone age, although they were highly developed.
Mesoamerica was much less likely than the Fertile Crescent to develop and diffuse a civilization. It did not have as many kinds of domesticable plants and animals. This made it harder to develop truly productive agriculture.
In addition, it is hard for anything to diffuse into or out of the region. Mesoamerica is on a long north-south axis, which is bad for diffusion. The Fertile Crescent, by contrast, is on a long east-west axis so diffusion is easy.
Because the Fertile Crescent had lots of domesticable species and because it was on a long east-west axis, it was likely to become a center for a civilization that would then spread.