Similarity metrics for text corpora are becoming critical due to the tremendous growth in the number of generative models. These similarity metrics measure the semantic gap between human and machine-generated text on the corpus level. However, standard methods for evaluating the characteristics of these metrics have yet to be established. We propose a set of automatic measures for evaluating the characteristics of semantic similarity metrics for text corpora. Our measures allow us to sensibly compare and identify the strengths and weaknesses of these metrics. We demonstrate the effectiveness of our evaluation measures in capturing fundamental characteristics by comparing it to a collection of classical and state-of-the-art metrics. Our measures revealed that recent metrics are becoming better in identifying semantic distributional mismatch while classical metrics are more sensitive to perturbations in the surface text levels.