Model-based approaches (e.g. maximum likelihood, Bayesian inference) are widely used with molecular data, where they might be more appropriate than maximum parsimony for estimating phylogenies under various models of molecular evolution. Recently, there has been an increase in the application of model-based approaches with morphological (mainly fossil) data; however, there is some doubt as to the effectiveness of the model of morphological evolution. The input parameters (prior probabilities) for the model are unclear, particularly when concerned with unobserved character states. Despite this, some systematists are suggesting superiority of these model-based methods over maximum parsimony based on, for example, increased resolution or, in the current study, the preferred phylogenetic placement of an iconic taxon. Here, we revisit a recently published analysis implying such superiority and document the discrepancies between parsimony-based and model-based approaches to phylogeny estimation. We find that although some taxa are shifted back to their “traditional” phylogenetic placement, other clades are disturbed. The model-based phylogenies are better resolved; however, due to the lack of an appropriate model of morphological evolution, the increase in resolving power is probably not meaningful. Similarly, some of the preferred phylogenetic positions of taxa, particularly of labile taxa such as Archaeopteryx, are based solely on analyses employing maximum parsimony as the optimality criterion. Poor resolution and labile taxa indicate a need for further examination of the morphology and not a change in method.