Species diversity versus phylogenetic diversity: A practical study in the taxonomically difficult genus Dactylorhiza(Orchidaceae), Biological Conservation 2006, 129 (1): 4-13.
They found that their results show that phylogenetic analyses and genetic data obtained with molecular tools can offer an alternative measure of biodiversity that is not sensitive to taxonomic inflation.
There are a vast of different measurements of phylogenetic diversity. I am afraid that regional or even global patterns are not available for many species until now.
In one of our studies, however, we found that (phylo)genetic diversity is probably not a suitable predictor of ecosystem functioning (Steudel et al. 2016, New Phycologist).
The data set would be great, but I think it first needs to be sampled to conduct such a study.