Different facets of biodiversity other than species numbers are increasingly appreciated as critical for maintaining the function of ecosystems and their services to humans. While new international policy and assessment processes such as the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) recognize the importance of an increasingly global, quantitative and comprehensive approach to biodiversity protection, most insights are still focused on a single facet of biodiversity-species. Here we broaden the focus and provide an evaluation of how much of the world's species, functional and phylogenetic diversity of birds and mammals is currently protected and the scope for improvement. We show that the large existing gaps in the coverage for each facet of diversity could be remedied by a slight expansion of protected areas: an additional 5% of the land has the potential to more than triple the protected range of species or phylogenetic or functional units. Further, the same areas are often priorities for multiple diversity facets and for both taxa. However, we find that the choice of conservation strategy has a fundamental effect on outcomes. It is more difficult (that is, requires more land) to maximize basic representation of the global biodiversity pool than to maximize local diversity. Overall, species and phylogenetic priorities are more similar to each other than they are to functional priorities, and priorities for the different bird biodiversity facets are more similar than those of mammals. Our work shows that large gains in biodiversity protection are possible, while also highlighting the need to explicitly link desired conservation objectives and biodiversity metrics. We provide a framework and quantitative tools to advance these goals for multi-faceted biodiversity conservation.