I would argue that Britain was much more successful in North America, considering that Canada still accepts the Queen as head of state. Depending how you measure it, British rule in India did not last nearly as long as in the 13 colonies either. Direct British control in India didn't begin until the late-1850s. Before that, from around 1757, a large portion of the country was ruled by the British East India Company, while another significant portion was ruled by Indian princes. As a result of the First Indian Revolution from 1857-1858, Britain took direct control over Indian affairs. From that date, British control lasted less than one hundred years (1858-1948). In contrast, Jamestown was founded in 1607 and the United States declared independence in 1776.

How would you measure "success" though? The British did rule India longer, though parts of India were indirectly ruled through allied princely states. By the twentieth century, the British realized it was getting harder to stamp out nationalism and popular protests kept growing especially after World War I. British reprisals also became more violent.

As for the role of white settlers, you could argue settlers contributed to more violence. See Kenya and South Africa for instance.