There were many ways in which the various Native Americans were similar to one another and different from the European societies at the end of the 15th century. Since your question asks specifically about “culture” this answer will discuss only culture, rather than things like the economies of the two peoples. Let us look at two major differences.
Culturally, the main difference between Native Americans and Europeans was in the way their societies were held together. Native Americans tended to live in much small groups, hunting and gathering rather than farming. This meant that their culture was more egalitarian and was based more on personal relationships. Europe was moving towards an impersonal culture while the Native Americans continued to live in groups that were small enough that everyone knew one another, there were no huge differences in status, and personal relationships held society together.
Additionally, the culture of the Native Americans was much less organized and rationalized than that of Europe. In Europe, there were already institutions to organize society. There was, for example, the Catholic Church, which organized and held authority over all of society. In North America, at least, there were no such institutions. People lived their lives without as much institutionalized authority to organize their lives and tell them what to do.
In short, the typical Native American (particularly in North America) lived in a much less organized and hierarchical culture than the typical European did.