The perspective of personalized medicine for brain disorders requires efficient learning models for anatomical neuroimagingbased prediction of clinical conditions. There is now a consensus on the benefit of deep learning (DL) in addressing many medical imaging tasks, such as image segmentation. However, for single-subject prediction problems, recent studies yielded contradictory results when comparing DL with Standard Machine Learning (SML) on top of classical feature extraction. Most existing comparative studies were limited in predicting phenotypes of little clinical interest, such as sex and age, and using a single dataset. Moreover, they conducted a limited analysis of the employed image pre-processing and feature selection strategies. This paper extensively compares DL and SML prediction capacity on five multi-site problems, including three increasingly complex clinical applications in psychiatry namely schizophrenia, bipolar disorder and Autism Spectrum Disorder (ASD) diagnosis. To compensate for the relative scarcity of neuroimaging data on these clinical datasets, we also evaluate three pre-training strategies for transfer learning from brain imaging of the general healthy population: self-supervised learning, generative modelling and supervised learning with age. Overall, we find similar performance between randomly initialized DL and SML for the three clinical tasks and a similar scaling trend for sex prediction. This was replicated on an external dataset. We also show highly correlated discriminative brain regions between DL and linear ML models in all problems. Nonetheless, we demonstrate that self-supervised pre-training on large-scale healthy population imaging dataset (N ≈10k), along with Deep Ensemble, allows DL to learn robust and transferable representations to smaller-scale clinical datasets (N ≤ 1k). It largely outperforms SML on 2 out of 3 clinical tasks both in internal and external test sets. These findings suggest that the improvement of DL over SML in anatomical neuroimaging mainly comes from its capacity of learning meaningful and useful abstract representations of the brain anatomy, and it sheds light on the potential of transfer learning for personalized medicine in psychiatry.