The next big task for the Chinese Communist Party is to do something without precedent: to give the entire country a first world standard of living without giving up its arbitrary power over the legal system and the economy. I think the South Korean system could be a plausible starting point; just substitute the privately-owned chaebols for the Chinese state-owned enterprises, and you are a part of the way there.
As far as I know, Xi isn’t interested in my advice. Otherwise, the Chinese and the South Koreans don’t have a lot of issues except for North Korea. There will always be limits on the closeness of the relationship unless and until the Chinese can somehow bring North Korea under control.