Of these two words, “assimilation” is the more appropriate. Some might argue that “extermination” is also appropriate, but it is not nearly as appropriate as “assimilation.” The reason for this is that assimilation was an actual government policy while extermination never was.
There were, of course, people who would have liked to see all Native Americans dead. However, this was not what the government was trying to do. The wars against Native Americans and the killing of the buffalo were not meant to kill all Native Americans but rather to force them off of lands that whites wanted. This is not the same as extermination.
There was, by contrast, a true effort to assimilate the Native Americans. They were sent to boarding schools and made to speak English and otherwise let go of native ways. The Dawes Severalty Act did try to destroy the communal way of life and make Indians into small farmers. This was a government policy explicitly created and carried out. Therefore, “assimilation” is a much more appropriate word than “extermination.”