Most of the existing Information Retrieval (IR) metrics discount the value of each retrieved relevant document based on its rank. This statement also applies to the evaluation of diversified search: the widely-used diversity metrics, namely, α-nDCG, Intent-Aware Expected Reciprocal Rank (ERR-IA) and D#-nDCG, are all rank-based. These evaluation metrics regard the system output as a list of document IDs, and ignore all other features such as snippets and document full texts of various lengths. In contrast, the U-measure framework of Sakai and Dou uses the amount of text read by the user as the foundation for discounting the value of relevant information, and can take into account the user's snippet reading and full text reading behaviours. The present study compares the diversity versions of U-measure (D-U and U-IA) with the state-of-the-art diversity metrics using the concordance test: given a pair of ranked lists, we quantify the ability of each metric to favour the more diversified and more relevant list. Our results show that while D#-nDCG is the overall winner in terms of simultaneous concordance with diversity and relevance, D-U and U-IA statistically significantly outperform other state-of-the-art metrics. Moreover, in terms of concordance with relevance alone, D-U and U-IA significantly outperform all rank-based diversity metrics. Thus, D-U and U-IA are not only more realistic but also more relevance-oriented than other diversity metrics.