There is increasing expectation that advanced, computationally expensive machine learning techniques, when applied to large population-wide neuroimaging datasets, will help to uncover key differences in the human brain in health and disease. We take a comprehensive approach to explore how multiple aspects of brain structural connectivity can predict sex, age, general cognitive function and general psychopathology, testing different machine learning algorithms from deep learning model (BrainNetCNN) to classical machine learning methods. We modelled N = 8, 183 structural connectomes from UK Biobank using six different structural network weightings obtained from diffusion MRI. Streamline count generally provided highest prediction accuracies in all prediction tasks. Deep learning did not improve on prediction accuracies from simpler linear models. Further, high correlations between model coefficients from deep learning and linear models suggested similar decision mechanisms were used. This highlights that model complexity is unlikely to improve detection of associations between structural connectomes and complex phenotypes.