Birth-death models (BDMs) are stochastic processes describing the processes of speciation and extinction through time and across taxa and are widely used in biology for inference of evolutionary timescales. Previous research has highlighted how the expected trees under BDMs tend to differ from empirical trees with respect to indices such as the amount of phylogenetic imbalance. However, our understanding of how trees differ between BDMs and empirical inferences remains incomplete. In this study, we demonstrate how four different constant-rate BDM scenarios influence tree shape and branch-length characteristics of phylogenetic trees, using a wide range of topology and branch-length indices. Comparison of BDM expectations against a comprehensive empirical dataset of 1,189 empirical trees shows that the dominant form of model inadequacy in BDMs is in failing to accommodate large amounts of phylogenetic imbalance in empirical processes. We also find that empirical trees tend to have significantly greater depth, lower stemminess, and longer shortest pendant edge lengths than BD-simulated trees. The results also indicate that accounting for the sampling fraction is the single most important parameter for accommodating empirical stemminess and branch lengths. Overall, our findings demonstrate the limitations of BDM priors when inferring the shape and structural characteristics of phylogenetic trees, highlighting the importance of novel methods that account for a broader tree space and secondarily reduce any possible bias in branch length estimation.