The relationship between morphology, connectivity, and function is a central challenge in neuroscience. The possibility of predicting neuronal function from morphology and connectivity has motivated the field to produce connectomes for increasingly complex organisms. With the recent completion of multiple connectomes of the Drosophila brain[1][2], we now assess, at scale, the quality of connectome-derived functional predictions. By measuring feature selectivity in more than 90 cell types in the fly visual system and leveraging a pair of recently annotated optic lobe connectomes[2][3], we evaluate which functional properties are well described by neuronal connectivity and morphology, and which are not. We demonstrate that orientation selectivity, direction selectivity, and spectral preference can be accurately predicted from the connectome. In contrast, we discover that receptive field size cannot be predicted by the retinotopic coverage of a neuron’s arbor. We also consider core assumptions of predictive connectomics, finding that postsynapse density predicts response amplitude at the level of whole cells, as well as the temporal correlation between pre- and postsynaptic partners at the level of individual connections. We further demonstrate that postsynaptic responses are poorly described by a connection-weighted sum of input activity. Instead, we find that strong inputs are more functionally homogeneous than expected by chance, and therefore exert an outsized influence on postsynaptic activity. Finally, we use a clustering analysis to show that similar connectivity does not predict similar physiology. Intriguingly, we find that the inverse model is valid – similar physiology can indeed predict similar connectivity. Asymmetries in the distributions of distances between cell types in high-dimensional connectivity and function spaces underlie the non-invertibility of this relationship. Our results both confirm and challenge some of the fundamental assumptions of predictive connectomics, and establish a new quantitative framework that may improve the accuracy of future connectome-inspired models.