I would say 중시하다 and 중요시하다 are interchangeable in most cases. They have the same basic meaning. A small difference is that 중시하다 probably sounds a bit more formal and might be a better choice than 중요시하다 for literary contexts or when talking about heavy subjects. 중요시하다 seems better suited for more concrete and practical things. So my choice on your examples would be as follows (although none of them are wrong). - 외모를 중요시하다 / 중시하다. (no preference) - 보수주의자들은 자유를 중시한다. - 상품을 개발할 때 체감 나이를 중시해야 한다.