Cloud computing has revolutionized modern IT infrastructure, with virtualization technologies playing a crucial role in efficient resource utilization and deployment. Docker containers and Virtual Machines (VMs) are two dominant virtualization approaches, each presenting unique security implications. While Docker enhances agility, scalability, and resource efficiency, its shared kernel model introduces security risks, such as kernel exploits, container escape attacks, and privilege escalation vulnerabilities. In contrast, VMs offer robust isolation, mitigating risks through complete OS separation but at the cost of increased resource consumption and management complexity. This study presents a comprehensive analysis of security concerns associated with Docker and VMs, highlighting their attack vectors, vulnerabilities, and best practices for mitigating risks. Security architecture considerations, including hypervisor hardening, namespace isolation, and role-based access control, are explored. Additionally, hybrid approaches, such as running Docker inside VMs, are discussed as viable solutions to balance performance and security. Findings from this research emphasize the importance of tailored security strategies based on operational requirements. High-security industries, such as healthcare and financial services, may favor VMs due to their strong isolation properties, while development and CI/CD pipelines benefit from Docker's efficiency. Security automation, AI-driven anomaly detection, and confidential computing are identified as key areas for future advancements in securing virtualized workloads. By understanding the risks and implementing robust security frameworks, organizations can optimize both security and performance in their cloud infrastructure.