Logistic regression and artificial neural networks are the models of choice in many medical data classification tasks. In this review, we summarize the differences and similarities of these models from a technical point of view, and compare them with other machine learning algorithms. We provide considerations useful for critically assessing the quality of the models and the results based on these models. Finally, we summarize our findings on how quality criteria for logistic regression and artificial neural network models are met in a sample of papers from the medical literature.