Growing interest in understanding ecological patterns from phylogenetic and functional perspectives has driven the development of metrics that capture variation in evolutionary histories or ecological functions of species. Recently, an integrated framework based on Hill numbers was developed that measures three dimensions of biodiversity based on abundance, phylogeny and function of species. This framework is highly flexible, allowing comparison of those diversity dimensions, including different aspects of a single dimension and their integration into a single measure. The behavior of those metrics with regard to variation in data structure has not been explored in detail, yet is critical for ensuring an appropriate match between the concept and its measurement. We evaluated how each metric responds to particular data structures and developed a new metric for functional biodiversity. The phylogenetic metric is sensitive to variation in the topology of phylogenetic trees, including variation in the relative lengths of basal, internal and terminal branches. In contrast, the functional metric exhibited multiple shortcomings: (1) species that are functionally redundant contribute nothing to functional diversity and (2) a single highly distinct species causes functional diversity to approach the minimum possible value. We introduced an alternative, improved metric based on functional dispersion that solves both of these problems. In addition, the new metric exhibited more desirable behavior when based on multiple traits.