A relatively large number of studies have investigated the power of structural magnetic resonance imaging (sMRI) data to discriminate patients with schizophrenia from healthy controls. However, very few of them have also included patients with bipolar disorder, allowing the clinically relevant discrimination between both psychotic diagnostics. To assess the efficacy of sMRI data for diagnostic prediction in psychosis we objectively evaluated the discriminative power of a wide range of commonly used machine learning algorithms (ridge, lasso, elastic net and L0 norm regularized logistic regressions, a support vector classifier, regularized discriminant analysis, random forests and a Gaussian process classifier) on main sMRI features including grey and white matter voxel-based morphometry (VBM), vertex-based cortical thickness and volume, region of interest volumetric measures and wavelet-based morphometry (WBM) maps. All possible combinations of algorithms and data features were considered in pairwise classifications of matched samples of healthy controls (N = 127), patients with schizophrenia (N = 128) and patients with bipolar disorder (N = 128). Results show that the selection of feature type is important, with grey matter VBM (without data reduction) delivering the best diagnostic prediction rates (averaging over classifiers: schizophrenia vs. healthy 75%, bipolar disorder vs. healthy 63% and schizophrenia vs. bipolar disorder 62%) whereas algorithms usually yielded very similar results. Indeed, those grey matter VBM accuracy rates were not even improved by combining all feature types in a single prediction model. Further multi-class classifications considering the three groups simultaneously made evident a lack of predictive power for the bipolar group, probably due to its intermediate anatomical features, located between those observed in healthy controls and those found in patients with schizophrenia. Finally, we provide MRIPredict (https://www.nitrc.org/projects/mripredict/), a free tool for SPM, FSL and R, to easily carry out voxelwise predictions based on VBM images.