America's economy is bigger and more battle hardened. China's has holes through it. Both rely heavily on each other and if this goes on it will cause enormous troubles globally. In a race to catastrophe, China hits rock bottom first is my guess.
It's hard to predict who backs down. Both are now led by populist, right leaning strong men who need to appear powerful.
Worst case scenario? Nobody backs down, a global recession occurs and China arms up, dividing the globe into two economically. Some countries willingly join their new economic coalition, while others nearby are threatened into it with military action or outright taken over. Neighbours immediately around China are the most likely to join, willing or not. Russia and other declared enemies of the US are obviously guaranteed entrants. Two new global economies form: China and their allies, and US and their allies.
Best case scenario? Everyone calms the fuck down for a bit and it goes back to normal.