It is already too bad that the US's plan to get to the moon was so flawed that it has been delayed again and again and money was wasted.
Let's imagine that China puts people on the moon next year in a method similar to the way the US did it in 1969 (but probably better in some ways). They still are mostly doing something that has been done before by the USA.
In that same year, the USA will probably continue to launch 80% of the rockets to space. Maybe we don't do our next trip to the moon for another five years. But there's good chance by then we will be using much more advanced and reusable rockets. Does that really make the US behind?
I want to see us invest more into space exploration. I think its sad that NASA's plan has been dumb. But getting two or three people to the moon is more about showing that China is capable (which is a very reasonable goal for them) then showing they have some long term advantage.