This paper provides a comprehensive review and strategic framework to navigate this complex ecosystem of open-source and proprietary models for healthcare. We analyze the technical capabilities, implementation challenges, and governance requirements of both AI paradigms through a systematic and organnized survey of current literature and emerging trends. Our findings indicate that while open-source models offer superior transparency, customization, and data privacy—increasingly rivaling proprietary performance in diagnostics—proprietary systems maintain advantages in reliability, support, and integration. However, AGI also introduces complex risks ranging from algorithmic bias (if uncontrolled) to regulatory fragmentation (lack of regulation). Evidence shows concerning patterns in automated decision appeals and significant financial barriers to implementation that could limit accessibility. To address these challenges, we propose a tiered risk-management and governance framework that synthesizes the strengths of both open and closed-source approaches. Our recommendations include the adoption of international certification protocols aligned with global explainability standards, federated learning architectures to ensure privacy while enabling collaboration, and adaptive policymaking to balance innovation with patient safety. This integrated approach aims to maximize the benefits of both open-source and proprietary AI while focusing on remodification of unique risks posed by agentic systems.