COVID-19, an infectious coronavirus disease, caused a pandemic with countless deaths. From the outset, clinical institutes have explored computed tomography as an effective and complementary screening tool alongside the reverse transcriptase-polymerase chain reaction. Deep learning techniques have shown promising results in similar medical tasks and, hence, may provide solutions to COVID-19 based on medical images of patients. We aim to contribute to the research in this field by: (i) Comparing different architectures on a public and extended reference dataset to find the most suitable; (ii) Proposing a patient-oriented investigation of the best performing networks; and (iii) Evaluating their robustness in a real-world scenario, represented by cross-dataset experiments. We exploited ten well-known convolutional neural networks on two public datasets. The results show that, on the reference dataset, the most suitable architecture is VGG19, which (i) Achieved 98.87% accuracy in the network comparison; (ii) Obtained 95.91% accuracy on the patient status classification, even though it misclassifies some patients that other networks classify correctly; and (iii) The cross-dataset experiments exhibit the limitations of deep learning approaches in a real-world scenario with 70.15% accuracy, which need further investigation to improve the robustness. Thus, VGG19 architecture showed promising performance in the classification of COVID-19 cases. Nonetheless, this architecture enables extensive improvements based on its modification, or even with preprocessing step in addition to it. Finally, the cross-dataset experiments exposed the critical weakness of classifying images from heterogeneous data sources, compatible with a real-world scenario.