How were the Native Americans and White people depicted in The Searchers and Dances with Wolves?

You are accurate in suggesting that both films depict each
group opposite of one another.  In Ford's work, Native Americans are shown as savage
terrorists while justice and honor have to be instilled by white men.  In this
depiction, the Native Americans lure the men away from their homes, savagely kill their
families, and commit wrong.  It is the white men who have to painstakingly hunt down the
Indians to restore justice, righting the wrongs that have been done.  Native Americans
are depicted as a demonizing form of "the other," a force to which fear and repression
can be the only responses.  Costner's work almost inverts this.   White society is the
demon while the Native Americans are apotheosized.  In the end, I think that both films
capitulate to stereotypes of different time periods.  The 1950s sought to present a very
consensus driven vision of American History in which Native Americans would be the
"other" that contradicts the established vision of American exceptionalism.  The late
1980s was a period where the diversity of narratives began to emerge, contributing to a
conflict based expression of American History where the established "consensus" based
aspect had undergone significant revision.