Sorry but China and the Mughals can't hold a candle to the, for mankind immensely important, scientific breakthroughs made in Europe during the enlightenment. More scientific discoveries were probably made 1700 - 1800 in Europe and its colonial off-shots than in the entire scientific history of China. And then there is philosophy too, with social ideas that affect us even to this day on a daily basis...
And if are talking purely about political relevance, the only continent where China had relevancy in everyday politics of nations during the EU era was in Asia. On every other continent, Europe had a stronger presence. And later during the era, Europe became more relevant to many Asian nations as well, perhaps even the majority.
You have no idea what you are talking about.
Europe didn't become important until the mid-to-late 1850s. Even at the beginning of the 1800s, China far eclipsed Europe in it's entirety. China was by and far the largest producer goods on the planet and had a comparatively modern army capable of challenging European powers with ease. The majority of the world's trade goods came from China or were channeled through China for pretty much the entirety of the period. As was much knowledge and science, as China was one of the world's main innovators until the late 18th and 19th centuries.
What really killed China's position as the greatest world power was the industrial revolution which allowed Europe to compete with China in terms of production.
The Mughals as well, far outclassed any nation in Europe, and they fell more to internal issues than anything else.
Yes, in the long run Europe turned out to be "more important" (although even this was itself after
centuries of feeding off of China and knowledge passed down through trade and the silk road), but most of that didn't even take place until nearing the very end/just after the EUIV time period.
EDIT: meant mid-to-late 1800s. But the general point stands.
