Polyploidy, or whole genome duplication, has been an important feature of eukaryotic evolution. This is especially true in flowering plants, where all extant angiosperms have descended from polyploid species. Here we present a broad comparative analysis of the effect of polyploidy on flowering plant diversity. We examine the widely held hypothesis that polyploid flowering plants generate more diversity than their diploid counterparts, by fitting stochastic birth/death models to observed ploidal frequency data from 60 extant angiosperm genera. Our results suggest the opposite, that diploids speciate at higher rates than polyploids, through a combination of simple diploid speciation and tetraploidy. Importantly, the estimated diploid advantage stemmed primarily from a higher rate of polyploidization in diploids than polyploids. Our model is also able to account for the empirically observed correlation between polyploidy and species richness without assuming that polyploids have a speciation advantage over diploids.