Insider knowledge? Not really, unless you count asking actual chinese and taiwanese nationals what they think about it instead of assuming their world view is the same as my own.
The CCP primarily wants to gain power. Political, economic, and social. The levels of ambition probably vary by individuals inside the party, but generally involves a uniform level of control across all regions of China (including Taiwan from their point of view), and enough global power to give them a free hand in East Asia.
Chinese nationals may put more emphasis on increasing prosperity. Taiwan nationals may put more emphasis on strict control and global power. Individual reactions largely vary. Out of both groups, limitations on personal liberties cause the harshest criticism of CCP, with the one child policy almost universally seen unfavorably.