Which values do we need to lose, and which do we need to gain?
What aspects of the PRC's system should we emulate? I see few, if any.
In the US, battles between the governed and the governing were going on as early as 1792, when Jefferson emerged as the leader of the opposition. Further, the rancor we see now in US politics is far from unprecedented. As a tiny sample: the sitting Vice President shot the sitting Secretary of Treasury and mortally wounded him, and we had a civil war in which about 600,000 people died.
I believe the recent uptick in political dissension is a normal and healthy aspect of US politics.
I feel like I've kind of already answered this.
I think the Internet is the game changer. Or, rather, the speed and slipperiness of information is the game changer. In 1776, there was no easy way for the British to manipulate the perceptions of the colonists on a massive scale. Details of Burr's slaying of Hamilton were controlled by the politicos who witnessed it. The average person didn't have access to as many resources. No teenager was taking a musket into a tailor's shop and killing five people in a few munutes. No terrorists from an ocean away were firing cannons into public squares.
As a result, I think the value we place in freedom will have to change. At the end of the day, no one wants to be free in a country that is unstable and crime ridden. Freedom is only valuable when survival and safety are secured. With global terrorism, political polarization, and, most importantly, the capability of media to inform people about every bad thing that happens all the time, everywhere, people are feeling less safe (even if the world is a safer place).
An increase in security (via, for example, internet censorship, immigration restrictions, loss of gun rights, imposition on public speech, etc) will become an increasingly attractive option, despite the loss of freedoms it would entail. I think these are the sorts of things we'll look to China for.
This, of course, has trickle down to education, business regulation, family life, etc. A change in values has systemic consequences.