The shape of neuronal morphologies plays a critical role in determining their dynamical properties and the functionality of the brain. With an abundance of neuronal morphology reconstructions, a robust definition of cell types is important to understand their role in brain functionality. However, an objective morphology classification scheme is hard to establish due to disagreements on the definition of cell types, on which subjective views of field experts show significant differences. The robust grouping of neurons based on their morphological shapes is important for generative models and for establishing a link between anatomical properties and other modalities, such as biophysical and transcriptomic information. We combine deep learning techniques with a variety of mathematical descriptions of neurons and evaluate the classification accuracy of different methods. We demonstrate that various methodologies, including graph neural networks, topological morphology descriptors, and morphometrics, consistently perform with the highest accuracy for a variety of datasets. Based on these methods, we present a robust classification of both inhibitory and excitatory cell types in the rodent cortex and propose a generalized scheme for a consistent classification of neurons into classes.