First of all, we must recognize that the answer to this cannot be the same for every colonized group. Different imperial powers acted differently. There were different levels of commitment to different areas. Therefore, the record is not the same for every colonized place.
Second, we must also recognize that we cannot know what would have happened had it not been for colonization. We can say, for example, that a colonial power started to build infrastructure where there had not been any before. But we cannot say what the native government would have done if allowed to remain independent. For an example of this, let us look to Japan. Japan was “backward” in many ways when “opened” by Commodore Perry in 1853. In the next 50 years, however, it became a modernized country and an important world power without having been colonized. It is possible that other countries could have modernized themselves without having to be colonized.
All of this said, it is at least arguable that colonization did some good in some places. It was the British, for example, who brought democracy to India. That country remains the world’s largest democracy. The US likewise brought democracy to the Philippines. It was the British who built railroads in India and the Americans who built modernized ports in the Philippines. The historian Niall Ferguson has argued that imperialism did improve health in places like India and in the French colonies in West Africa. (As for religious advancement, it certainly seems presumptuous to claim that the colonizers’ religion was somehow and “advance” over that of the colonized.)
So, it is clearly true that some colonizers brought some good things to the places that they colonized. However, this should not lead us to conclude that imperialism was necessarily a good thing.