You also have to account for population numbers. The whole of the European landmass is barely a 2/3 billion people mostly spread out, with near constant in-fighting. Maybe in one part of the southern mediterian cost someone has an idea on how to put a steam engine on a ship without sinking or fire. Good plan but they lack any insight into how a steam engine works beyond the most basic levels. Unfortunately the best expert nearby is still hundreds of miles away and his king is at war with the first man's king. So no contact can be made and the idea dies. That's not even accounting for the language and culture barriers.
China prospered by having enough smart people close together who could communicate ideas.
Mind you, some densely populated regions of Europe (Germanicas, Gaul, even Albion) haven't done well historically. It comes back to the backwardness of western catholicism, IMO.
And Europe's population is rapidly growing right now, I'm surprised you haven't heard. You wouldn't believe the problems Rome, Al-Andalus and Egypt are having with immigrants. I can't talk about the situation in China, Bengal, or Vijayanangar, though