China will not compete with any country in military. It develops military soley for defense purpose as China holds defensive military policy.
In fact, it is reasonable to say that Chinese Navy is ranked #2 now. Being #1 is meaningless to China. Defense homeland requires much less military budget to achieve.
The budget difference between China and the US in military spending, China rather spend those money to help its people in their education, healthcare and public facilities development, and anything direct beneficial to its people.
This is why China does not intend to compete for military #1, just stay close enough technologically for self defense is sufficient.
However, technologically (domestic and space) and economically, China will eventually work its way out to lead the world, not because China wants to lead the world, but with “China Speed”, it can’t help to reach leader position, which is just a natural phenomenon for China.