Both sustainability and strategic goals are realized in the course of implementing projects and in this way, projects are crucial for companies. Despite the growing importance of projects and the vast resources allocated to them, the success rates achieved by these projects are still considered low. Numerous reasons have been identified in the literature for why a project might succeed or fail, and it has also been revealed that a competent project manager is a key factor in this process. However, papers have mainly focused on analyzing the required competencies in general, while the sector involved is rarely considered. Thus, this paper investigates, within an exploratory framework, the success and failure rates of projects and project management competencies in Hungarian public- and private-sector organizations by using the Mann–Whitney test. Based on the results, the authors reject the idea that public-sector organizations perform better than those in the private sector, but the analysis of the data also revealed that there were differences in the perceived importance of skills in the two sectors. Customer orientation and business acumen were considered significantly more important in the private sector than in the public sector, based on the sample available. This study also revealed possible correlations among the knowledge areas and skills required. In addition to contributions to the understanding of project success, this paper can also help to improve the project management frameworks applied in public and private companies. Furthermore, the findings can be adapted for projects that require a special attribute, such as sustainability.