Several classes of robust and reliable quality metrics have been developed for mesh quality assessment. However, in the context of meshfree methods, well-established and robust metrics for evaluating point cloud quality are lacking. This absence poses a fundamental challenge in defining and assessing the quality of a point cloud. While various criteria exist for evaluating specific aspects, such as point regularity, the reliability and robustness of these metrics have not been systematically analyzed. In this work, we evaluate the robustness and reliability of existing quality metrics and introduce new ones. Relying on correlation analysis, which we consider an effective approach, we investigate the relationship between quality metrics and numerical errors, ranking the metrics accordingly. The highest-ranked metrics serve as the most robust and reliable criteria for point cloud quality assessment. To achieve this, we conduct extensive numerical experiments across a wide range of scenarios, including both elliptic and hyperbolic equations, 2D and 3D domains, and variations in numerical parameters. Our findings reveal that 6 quality metrics consistently provide high correlation with numerical error which can be consider reliable criteria for point cloud quality assessment. Additionally, we show that several commonly used metrics are poor accuracy indicators.