The complexity of software is increasing day by day due to the increase in the size of the projects being developed. For better planning and management of large software projects, estimation of software quality is important. During the development processes, complexity metrics are used for the indication of the attributes/characteristics of the quality software. There are many studies about the effect of the complexity of the software on the cost and quality. In this study, we discussed the effects of software complexity on the quality attributes of the software for open source and closed source software. Though, the quality metrics for open and closed source software are not distinct from each other. In this paper, we comparatively analyzed the impact of complexity metrics on open source and private software. We also presented various models for the management of the project complexity such as William’s Model, Stacey’s Agreement and Certainty matrix, Kahane’s Approach and UCP Model. Quality metrics here refer to the standards for the measurement of the quality of software which contains certain attributes or characteristics of the software that are related to the quality of the software. Certain quality attributes addressed in this study are Usability, Reliability, Security, Portability, Maintainability, Efficiency, Cost, Standards and Availability, etc. Both Open source and Closed source software are evaluated on the basis of these quality attributes. This study also recommended future approaches to manage the quality of project Open source and Closed source software and specify which one of them is mostly used in the industry.