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Purpose: This research aimed to explore whether different project management approaches (traditional, agile or hybrid) differentiate concerning their impact on project success, taking project success as multidimensional phenomena. In addition to this, the authors wanted to explore if specific project characteristics moderate these effects. Design/methodology/approach: The authors empirically addressed these on a sample of 227 project professionals worldwide. The exploratory factor analysis (EFA) of project success dimensions was done to validate these factors' constitution concerning their manifest variables. The K-means cluster method was used to distinguish respondents' profiles among agile, hybrid and traditional project management approaches. To test the significance among research groups, the research hypotheses were tested with ANOVA tests. Findings: The authors evidenced that the agile approach has a more significant positive impact concerning the two out of five dimensions of project success, under analysis in this research (impact on the team and preparing for the future), over the traditional approach. Practical implications: The research is relevant for project management practitioners to tailor the success-oriented project management approach and for academics to develop project management contingency theory. Originality/value: The authors constructed a research framework to test the impact and effectiveness of different project management approaches (traditional, agile, hybrid) on the dimensions of project success in different contextual conditions (organization industry, project type, novelty, technology, complexity and pace). The paper's main contribution is to expand data on the impact of these approaches on project success and compare them with relevant results and findings of previous research. © 2022, Emerald Publishing Limited.