Hackathons have emerged as dynamic platforms for fostering innovation, collaboration, and skill development in the technology sector. Structural differences across hackathon formats raise important questions about how event design can shape student learning experiences and engagement. This study examines two distinct hackathon formats: a gender-specific (GS) hackathon and a regular institutional (RI) hackathon. Using a mixed-methods approach, we analyze variations in team dynamics, project themes, role assignments, and environmental settings. Our findings indicate that GS hackathons foster a collaborative and supportive atmosphere, emphasizing personal growth and community learning, with projects often centered on health and well-being. In contrast, RI hackathons tend to promote a competitive, outcome-driven environment, with projects frequently addressing entertainment and environmental sustainability. Based on these insights, we propose a hybrid hackathon model that combines the strengths of both formats to balance competition with inclusivity. This work contributes to the design of more engaging, equitable, and pedagogically effective hackathon experiences.