I know that when the RoC continued in Taiwan it was very authoritarian up until around the seventies or eighties I think. Now, it's got a fairly liberal regime and a very robust opposition party. On the other hand, the PRC has no democracy, no freedom of speech, an economy dominated by SOEs, and seemingly no chance of changing anytime soon.
Why did Taiwan change but not the PRC?
Chiang Kai-Shek died with his son as his successor, his son appointed a vice president who was more liberal, and there was a general shift to liberalism in the 80s and 90s throughout Asia. The Taiwanese government made a general move around there to become more liberal, opening up elections and ending martial law.
The PRC, however, is not interested in these reforms, and operates in a similar manner to how the Soviet Union operated, with all candidates being vetted heavily by the Communist Party over the years, and everyone in the upper echelons being very old and very loyal. They have found that it's much easier to maintain their economic growth and power by completely dominating the government, and stifling any chance of change which they don't like.