The construction industry, while contributing significantly to economic growth and social development, poses serious environmental issues through unsustainable resource use and substantial waste generation. The Circular Economy (CE) offers a promising solution by enhancing resource efficiency and reducing waste. However, its implementation within the construction sector is still developing and faces various challenges. This paper investigated the perceptual differences between public and private sector respondents in Vietnam regarding the importance of 16 factors for implementing CE practices in construction. Analysis of 104 qualified survey responses revealed that both sectors recognized “C01—The lack of a consistent legal framework” as the most significant challenge. A t-test at a 0.05 significance level indicated significant differences in seven factors, with private sector respondents scoring higher on issues related to profitability, such as raw material costs, end-of-life values, and supply chain fragmentation. In contrast, the public sector focuses more on standardization and social responsibility, aligning with their regulatory and public service priorities. Future research could benefit from using factor analysis to explore the underlying relationships between these factors and their impact on CE implementation.