European, and later American, treatment of Native Americans was not colonization, just straight-up genocide. It's not really relevant to the question of the long-term impact of British institutions in former colonies.

The biggest part of that genocide was accidental, and accomplished before the first permanent European settlements were ever established in North America. The story of Amherst's "smallpox blankets" is widely known, and deplorable, but the worst of the epidemics had raged through and decimated native populations in the 250 years prior since first contact.

It seems to be conveniently forgotten that many tribes were complicit in aiding and abetting Europeans in exterminating their rivals as well. Cortez conquered the Aztecs with 600 Spaniards... and 200,000 Tlaxcalans. The Iroquois confederation did most of the work of exterminating other native populations throughout the Great Lakes region.

The British were famous for divide and rule policies in India - that's how a little company like the east India company eventually swallowed up the various kingdoms and princely states of the subcontinent.