Africans and Europeans had already had some contact with one another for centuries, since it is possible to travel between the two continents by land or sea without crossing a whole ocean. In contrast, Native Americans were very isolated from Europe and Africa for thousands of years, as the landbridge that their ancestors traveled across flooded over and remained impassible. Still, many important differences between African and European cultures persisted into the era of European colonial expansion (and to some extent do still persist today).
Once Europeans began to colonize North America, they came into contact with Native Americans for the first time. While both cultures had many commonalities---they spoke language, they wore clothing, they used agriculture, they traded with their neighbors---there were radical differences in worldview between the colonists and the natives.
The colonists came from a society based on a mercantilist monetary economy, where one of the chief goals of entire countries was to extract and amass as much gold as possible. They also were predominantly believers in Christian religion, and sought to spread Christian religion wherever they landed.
The natives, on the other hand, lived primarily in tribal societies or intertribal coalitions (such as the Iroquois Confederacy), and did not use a monetary system or place any special value on precious metals. Native religions were predominantly animist, based on the worship of nature, animals, and human ancestors. While many assume that this worship of nature must have led to better ecological sustainability, it's not clear how much this was actually true; while in some ways Native American societies were ecologically sustainable (their forestry management was excellent), in other ways they were not (they caused a number of major extinctions of large animals).
African societies were in many ways similar to Native American societies in their structure, though they had much more extensive influences from Europe and Asia. Christianity and Islam were already influential in Africa by the 16th century, and African cultures were already somewhat accustomed to the trade of gold and gemstones. While Native Americans were primarily agricultural societies, a significant proportion of Africans were hunter-gatherers. Still, the basic tribal structure was typically quite similar, and the distinction between nomadic farmers and hunter-gatherers is not always very large.
The Christian and mercantilist ideas of Europeans had large, prolonged influences on both African and Native American cultures. Infamously, Europeans introduced new institutions of slavery, applied to both Native Americans and Africans. While both Native American and African cultures had forms of slavery prior to contact with Europeans, it was the application of European markets that expanded slavery into the global institution it became. Previously slaves were largely prisoners of war, traded for diplomatic reasons; after Europeans arrived they were treated as capital assets to be bought and sold on an open market.
Today we can see an almost total transformation of African and Native American worldviews effected by European ideas. Today, the majority of Native Americans and Africans are Christian. While some try to hold onto their ancient tribal structures, most African and Native American societies are now structured according to the European model of civil government and a money-based market. In the US we have become accustomed to Native American-owned casinos and banks---yet this could hardly be further from how Native Americans lived a thousand years ago.
Conversely, Europeans were not as heavily influenced by Native American and African worldviews. Hardly any adopted Native American religions, and they maintained their same basic structure of government and money-based markets, which eventually evolved into modern industrial capitalism. However, they could hardly avoid being influenced altogether. They learned many agricultural techniques from Native Americans, and restructured their diets to incorporate foods grown in North America such as corn and potatoes. Where Europeans brought the Native Americans alcohol, they received tobacco in return---and in both cases the new drug was thoroughly embraced.
Another potential Native American influence on European ideas relates to the US Constitution. While the U.S. certainly borrowed greatly from European ideas of democracy, some historians argue that it is possible that an additional influence may have come from the Iroquois Confederacy and its federalized system of central authority with certain powers delegated to smaller, local authorities.
