Ok well maybe this matters. I thought I was not vague about examples. I don't care about the game discussion anymore I know the game is meant to be pseudo-history.
What is complex society? If a city in North America was bigger than any in Europe at the corresponding time is that complex? Read the population estimate from this article.
http://en.wikipedia.org/wiki/Cahokia#Ancient_city
Low Estimates are 40,000.
Here is their diet.
If you do not think this is complex society then we will disagree. I don't have much time to discuss now though because I am back to a normal schedule.
This is actually very interesting. The population was estimated between 8,000 and 40,000 though, but nevertheless, it still had an extremely large population.
I do consider this a complex society, as I consider the Aztecs, Mayans, Incans and other large American empires to have had complex societies. But this complexity is only one of the many factors that caused Eurasians to be more advanced (I use this word for a lack of a better one, but they utilized many more technologies, and had many more goods than other societies).
Re: the agricultural side, I am sure that if the Mississipian civilization had not been exterminated by Eurasian diseases, that they would have developed many of the philosophical and technical advances that Europeans had. Given a thousand years, they would probably have found steel themselves, developed gunpowder, and who knows what else.
But, Eurasians had a head start with Agriculture, and thus complex societies, and arrived at these techs first. Mesopotamia provided an ideal situation, given many readily available domesticable plants native to that region, along with fertile soil, etc. where agriculture developed in 10,000 BC. The East - West axis (according to Jared Diamond) then allowed this 'package' of domesticable plants and annimals to quickly spread to the rest of the continent within a few thousand years.
This Mississipian culture did not truly begin to flourish until 1000 AD. This was likely due to the eventual arrival of corn from mesoamerica around the year 900AD (which spread very slowly due to the north-south orientaion of the continent), and other plants from locations I cannot care to research. They were then, intentionally or unintentionally, wiped out by Europeans who had attained this level of society much earlier.
For example Babylon is believed to have reached 200,000 inhabitants in the year 1671 BC. This gave Mesopotamia a two and half millenium head start. This, including the profound effect their culture had on Europeans, places them as more influential than the Mississipian culture imho.