Lets look at what it would really mean if China becomes the world's economically dominant country:
1. Chinese Yuan replaces the USD as the currency used in international business interactions.
2. Chinese, Mandarin ?, replaces English as the world's Lingua franca.
3. China becomes the dominant Pacific rim military power.
4. China's culture replaces the West in terms of music, art, movies, etc.
I doubt if 2, 4, and maybe 4 could happen without a complete collapse of the West. But if all 4 scenarios did happen I doubt it would mean the END OF THE WORLD.
Personally, I can not get feared up over an ascendant China or India. As someone pointed out earlier in this thread it could mean and probably would have to mean an improvement in the quality of life for a big chunk of the world's population.