During Dark and Middle Ages (and maybe during the time of Roman Empire as well), the Europeans were, arguably, less advanced technologically, militarily, culturally, and socially, than the Chinese. But, as we know, by the 20th century the Europeans have (again, arguably) outmatched the Chinese in all of those aspects.
So when was the "intermediate" periode happen? A period during both the Europeans and the Chinese were evenly matched? When?