From my perspective, the proper answer to your questions can come only if we step back from the emotions that both Trump and Xi elicit in many of the rest of us.
Having done that, it is then important to note that the United States is far from a perfect exemplar of democratic politics and public accountability.
The simple answer, in my view, is that this has become a clash of ideologies. Xi invested in this battle almost as soon as he assumed China's top leadership positions in late 2012 and early 2013. But the CPC has always had a core of leaders and senior ideologues who were resolute in their rejection of political pluralism and greater protection of individual rights and freedoms.
The United States has made a fetish of elections, often at the expense of having grown-up debates about the extent of oligarghic (or plutocratic) influence over policymaking. I've recently read some excellent commentaries about the baleful influence of the unreconstructed US Senate. It is profoundly undemocratic, at least in terms of the incredibly unequal distribution of influence per capita--take, for example, California and Rhode Island. Both have two seats in the Senate, despite the huge population disparity that distinguishes the one from the other.
Leaving aside these and other blemishes, however, the United States is still a democratic state with an independent (if also imperfect) judicial system that affords individuals the opportunity to push back against the depredations of the state or of powerful business interests.
China, on the other hand, is an increasingly totalitarian, one-party state where the governing party engages in huge self-aggrandizement and also runs roughshod over individuals and minority groups with impunity.
So, yes, an ideological conflict, to be sure.