A number of methods have recently become available to infer rates of speciation and extinction from datasets containing or restricted to extinct taxa; however, their comparative performance remains largely unexplored. To investigate the congruence of the estimates of macroevolutionary rates produced by these approaches, we inferred tip-dated phylogenies of bird-hipped dinosaurs (Archosauria: Ornithischia) using the Sampled-Ancestor Fossilized Birth-Death (SA-FBD) process and two of the largest character matrices published to date (73 taxa and 255 characters; 69 taxa and 380 characters). Phylogeny-based diversification rate analyses were performed using the recently released “fossil BAMM” (BAMM v2.6) package and a SA-FBD epoch model in BEAST 2. Importantly, no rate shifts were identified in the BAMM analyses, with the posterior probability of the zero-shift configuration ranging from 0.49 to 0.68, and ornithischian evolution was characterized by a single tree-wide density-dependent mode of diversification. Given the high congruence between the prior and posterior rate shift number distributions, we speculate that these findings may be driven by the insufficient number of included tips. A comparison with PyRate, a related Bayesian approach that does not rely on time-calibrated phylogenies, is also presented. We urge caution when applying BAMM-type macroevolutionary analyses to wholly extinct clades, as even the most comprehensive datasets available for extensively studied groups may not be large enough to detect diversification rate shifts.