China is a bigger threat to its close neighbors. But its lack of a global footprint is a major weakness compared to the US.
Although they are a communist country, China’s true attack vector is economic. In addition to propping up businesses so they can undersell competitors in other nations (illegally, but nobody is enforcing this), they have been aggressively making inroads in developing nations. They exploit the countries with poor populations and limited regulations (or no way to enforce them) to get cheap materials and establish a foothold there.
The shooting of two Zimbabwean workers by a Chinese boss shows the "systematic and widespread" abuse that locals face in Chinese mining operations, says the Zimbabwe Environmental Law Society (ZELA).
www.cnn.com
America’s global system of bases and its large number of alliances make it far stronger than China worldwide. A larger population doesn’t mean China can just win every war. You need to transport and deploy your forces strategically. America can deploy from just about anywhere on the globe. China can deploy from, well, China.
Of course, if people launch nukes, none of that will matter.
China's economic imperialism isn't simply classic economic exploitation (here, I speak/write from a perspective of some slight experience - in Africa and central Asia we (the EU) worked occasionally with China, and I had dealings with Chinese diplomats).
It is much more subtle than that.
Yes, much of it is about access to raw materials, and resources, and limited regulations, but the attraction of limited regulations goes both ways.
This is because the Chinese often offer the sort of no-strings-attached (or, no irksome human rights or oversight strings or conditions attached to aid, or economic support, of the sort that EU aid packages invariably include) economic support that is very attractive to some local elites, just as limited oversight of their activities - no tiresome labour rights or environmental awareness nonsense, for example - as a condition of aid - attaches to their own endeavours in third party countries in Africa and elsewhere.
Re a possible military threat: To my mind, the Chinese only express themselves militarily when the cost (to them) is likely to be limited, or the likelihood of success extraordinarily high - i.e. violence is a last resort.
My experience when speaking/meeting with them - my sense of them - was a deep (and profound, and, I would argue, genuine) reluctance to become embroiled in unnecessary, unprofitable, unwinnable, military adventures.
Therefore, such overt military threats as they pose, will tend to be confined to their own "sphere of influence", or regionally, - as
@SuperMatt says, they pose the greatest (military) threat to their near neighbours - where they believe that they have a right to exercise or project military power.
They can wield other - far more useful - weapons in their tool box, principally economic and/or cultural ones (such as access to domestic markets, denial of access, - participation in international markets, or not - conditions set re economic access, activity and ownership).