Accurately estimating uncertainties in neural network predictions is of great importance in building trusted DNNs-based models, and there is an increasing interest in providing accurate uncertainty estimation on many tasks, such as security cameras and autonomous driving vehicles. In this paper, we focus on the two main use cases of uncertainty estimation, i.e., selective prediction and confidence calibration. We first reveal potential issues of commonly used quality metrics for uncertainty estimation in both use cases, and propose our new metrics to mitigate them. We then apply these new metrics to explore the trade-off between model complexity and uncertainty estimation quality, a critically missing work in the literature. Our empirical experiment results validate the superiority of the proposed metrics, and some interesting trends about the complexity-uncertainty trade-off are observed.