in the rest of the continent?
It's universally accepted that the main reason to the decrease in native population was mainly due to illnesses, virus and bacteria brought by the Europeans to people not inmune to their exposure. What percentage of any decrease in their population was due to illness as opposed to slaying is, and will remain, a mistery, but the majority of scholars seem to agree that illnesses brought by Europeans account for up to 90 percent of the decrease, at least during the first years or even the first century.
But it still remains a fact that European powers massacred large numbers of natives. There is, nevertheless, a region that can give us some clue on how different natives were treated by different people. The region has kept reasonable census of people living there since the first Europeans arrived there to colonize. It has also been subject to studies and analysis on the accuracy of these censuses at different periods, and last, the region has been dominated by different colonizers. This region is California, where the Spaniards arrived and started to colonize it by mid 18th century, although some explorations took place earlier. In 1821, during the Mexican Independence, it became part of Mexico and, finally, America took control by 1848 (Treaty of Guadalupe Hidalgo).
The following image shows the native population of California at different dates (from Population of Native California as per Historical Demography. Handbook of North American Indians, by Sherburne F. Cook (1978):

1770 data shows the first numbers of natives in California, just after the Spaniards started colonizing it.
1830 shows the population just a few years after the independence of Mexico from Spain.
1845 shows the beginning of American rule in California.
1910 shows the lowest level of natives ever in California.
No doubt, in my opinion, America carried out more damage to the native population than Spain, even taking into account the possible decrease due to illnesses by first contact with Europeans during the 18th century.
Но с другой стороны Колумб и Ко на Эспаньоле тоже себя неплохо показали, хотя и раньше, гораздо раньше.