The interrelationships of the three major dinosaur clades (Theropoda, Sauropodomorpha, and Ornithischia) have come under increased scrutiny following the recovery of conflicting phylogenies by a large new character matrix and its extensively modified revision. Here, we use tools derived from recent phylogenomic studies to investigate the strength and causes of this conflict. Using both the original and rescored dataset, we examine the global support for alternative hypotheses as well as the distribution of phylogenetic signal among individual characters. We find the three possible ways of resolving the relationships among the main dinosaur lineages (Saurischia, Ornithischiformes, and Ornithoscelida) to be statistically indistinguishable and supported by nearly equal numbers of characters in both matrices. While the changes made to the revised matrix increased the mean phylogenetic signal of individual characters, this amplified rather than reduced their conflict, resulting in greater sensitivity to character removal or coding changes and little overall improvement in the ability to discriminate between alternative topologies. We conclude that early dinosaur relationships are unlikely to be resolved without fundamental changes to both the quality of available datasets and the techniques used to analyze them.