Several factors account for this difference.
First, on the American landmass, the indigenous inhabitants were relatively small in number compared to the population of Asia. The tragic fact of indigenous Americans lacking natural resistance to illnesses such as smallpox, which the Europeans were carriers of, accounts for a huge number of them being wiped out by disease even before they were subjected to deliberate genocidal attempts by the invaders.
Second, in taking over or making colonies of Asian lands, the European intention primarily was not to migrate to or settle those lands themselves. In India, for instance, the British were not interested in establishing colonies of their own people but were concerned with the natural resources of the country they could trade with and (more exactly) exploit or steal from. They sent missionaries to India, but this was a small-scale effort in comparison with their commercial and kleptocratic interests on the Subcontinent. Hinduism and Buddhism had been established before the advent of Christianity, and Islam has throughout its existence been a religion whose adherents have seldom allowed themselves to be converted to another religion or swayed to abandon their faith. The Asian nations thus retained their long-established religions.
By contrast, the Spanish, Portuguese, and English regarded the American continent as a place where they could send their own people in large numbers to establish colonies and create an extension of European civilization. In Latin America there was large-scale intermixing between the whites and the indigenous people, and today, approximately two-thirds of the population are mestizos. Though this did not occur to anywhere near the same degree in North America, the English had the implicit belief that it was their destiny to conquer: that the land had been granted to them much as God had given the Israelites the land of Canaan. The American Indians lacked the manpower, weaponry, and resources to fight back the European invasion. The same was true of the aborigines in Australia and New Zealand. In addition, in both America and Oceania, the Europeans had no scruples against first rounding up and deporting to the interior large numbers of the indigenous people, and then massacring them as they did in genocidal numbers. The Tasmanian aborigines are an example of a genocide that was completely accomplished, as all the remaining members of the ethnic group were hunted down and exterminated. These kinds of actions would have been logistically impossible in Asia even if the Europeans had had such intentions there.