But, in North America, at least, the leading cause of death was an epidemic of smallpox from 1775 to 1782 that raced ahead of European colonists from the Atlantic Coast to the Pacific Coast.
This epidemic was not intended by the colonists as a means of destroying the existing population, nor was it even really well understood. While the germ theory of disease had been proposed at that point, it was not widely accepted.
This isn't to say that Europeans did right by Native Americans before or after this epidemic. But, the bulk of the Native American deaths caused by the Europeans in North America were due to the inadvertent spread of diseases to which Native American populations never exposed to them were far more vulnerable than Europeans who had 8,000 years or so of natural selection at work building their immune systems' ability to defend against these diseases. And, the military superiority of Europeans in the century or so of conquest called "the Indian Wars" that followed, had as much to do with the residual impacts of this devastating loss of life due to new infectious diseases as it did to do with weapons or tactics.