Think China has some way to go before it becomes as powerful as US(circa 2030).
However US will have the edge as it has rich and powerful allies and most people prefer US culture to Chinese culture.
Chinese weakness is lack of true allies...it has none, it is surrounded by enemies, and this is due to Chinese blunders..
it has made some progress recently but all of it is mostly investments, not strategic ties...
only exception is Pakistan, which is by far a weak country...
so if in 20 years, even if china economy doubles that of USA(wont happen ever due to older population in china, china is still behind USA in nominal GDP) it would still not be able to challenege USA as US allies are strong..
look at Japan, Korea, Germany , europe, austrialia and now both india and vietnam(emerging economic might)
what china needs is immediate focus on two things
1. arrest its older population by scrapping the one child policy AND ALLOWING minorities to have more rights so the population boom can come from poor areas rather than richer areas(which wont happen even if china wants it)
2. Create solid investments and development plans in its choosen allies(like warshaw pack, and marshel plan), it needs to assess countries that are either neutral or pro china and than invest in them and give them access to its market..
examples are
pakistan
srilanka
myanmur
nepal
and african states
3. solve it issues withe neighboring countries, china is basically at war with every neighboring country sane Pakistan and nepal...it has created issues in south china sea as well
4. if china does address these issues it fate might not be different than soviet union too (doesnt seem like that now but you need allies)