I would argue that the lead in European colonial expansion passed to Great Britain in the years after 1600. Other countries such as Holland and France were important as well, but I think that Britain is the best answer to this question.
Before 1600, Spain was the leader. The Spanish colonization of the New World as well as of the Philippines gave it a large and rich empire. After 1600, though, England became much more important. After 1600, the British colonization of North America began. This would come to be a very important source of British wealth and power. The same was true as Britain began to expand its presence in India.
After 1600, the British Empire started to grow until it became the biggest empire in the world. Therefore, I think that Britain took the lead in colonization after 1600.
After the 16th century, the lead in European colonial expansion no longer belonged to Spain. Instead, the lead in this expansion passed to England. It was England that started to colonize North America, for example. It was also in the first half of the 17th century that Britain started to set up trading posts in India. This would begin the process of British domination of the Indian subcontinent. This was the beginning of the creation of the British Empire. Of course, Britain had plenty of competition. However, if any one country can be said to have taken the lead, it would be Britain.