Latent personality traits underpinning observed behavioral variation have been studied in a great many species. However, a lack of standardized behavioral assays, coupled to a common reliance on inferring personality from a single, observed, behavioral trait makes it difficult to determine if, when, and how conclusions can be directly compared across taxa. Here, we estimate the among-individual (co)variance structure (ID) for a set of four behaviors expressed in an open field trial, putatively indicative of boldness, in seven species of small freshwater fish. We show that the ID matrices differ in terms of the total amount of variation present, and crucially the orientation, and as a consequence, biological interpretation of the first eigenvector. Specifically, loading of observed traits on the main axis of variation in ID matched a priori expectations for a shy-bold continuum in only three of the seven cases. Nonetheless, when the ‘shape’ of the matrices was compared in higher dimensions, there was a high level of similarity among species, and weak evidence of phylogenetic signal. Our study highlights the present difficulty of trying to compare empirical inferences about specific personality traits across studies. However, it also shows how multivariate data collection and analysis allows the structure of behavioral variation to be quantitatively compared across populations or species without reliance on ambiguous verbal labels. It also suggests that the field may have much to gain from greater uptake of phylogenetically informed comparative approaches when seeking to test evolutionary hypotheses about the origin and maintenance of personality variation.