I was asked this question on Quora and here is my response:
The US and China are both large, great nations with patriotic populations. They will be “cooperative competitors” in the years to come.
From the China side, there are clearly elements that wish to overtake the US as a world leader, others that want to have a robust China with more of a regional leadership role, and still others that have a more peaceable cooperative focus.
From the US side, there are groups that want to fully engage China and see it become a partner on the world stage, others that want China to take on a greater global role in moderation and others that want to contain China.
There is no crystal ball of what the future will be. A lot depends on the economic, social and military developments in each country, as well as in Asia overall. Under President Xi Jinping China is getting more confident and/or aggressive depending on how you view things, as evidenced by Beijing flexing its muscles in the South China Sea, the setting up of the Asia Infrastructure Investment Bank as an alternative to the World Bank and ADB and the New Silk Road initiative (recently referred to as One Belt, One Road) to link China to Central Asia and Europe by land.
From the US side, the country wants to have China more engaged in global institutions, but does not want to have its own soft and hard power eroded. The US will continue to be the dominant global power, but it is not so easy to share the stage.
Personally, I expect the two countries to be “cooperative competitors.” Each will focus on its own national interest. At times these will overlap (for example, in the hoped for environmental pact coming out of the Paris meetings later this year), at times there will be uncomfortable situations (as in the AIIB and World Bank) and there is always a real potential for open conflict to erupt. What is clear is that there will be greater engagement between the two countries, missteps by both sides as the relationship matures and continued growth in business and investment flows between the countries.
Being an optimist, I hope that each country recognizes the strengths and weaknesses in the other and understands that while they may never be close friends, they can accomplish a great deal more working in concert than as opponents.