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In this work, the performance of five deep learning architectures in classifying COVID-19 in a multi-class set-up is evaluated. The classifiers were built on pretrained ResNet-50, ResNet-50r (with kernel size 5×5 in the first convolutional layer), DenseNet-121, MobileNet-v3 and the state-of-the-art CaiT-24-XXS-224 (CaiT) transformer. The cross entropy and weighted cross entropy were minimised with Adam and AdamW. In total, 20 experiments were conducted with 10 repetitions and obtained the following metrics: accuracy (Acc), balanced accuracy (BA), F1 and F2 from the general Fβ macro score, Matthew’s Correlation Coefficient (MCC), sensitivity (Sens) and specificity (Spec) followed by bootstrapping. The performance of the classifiers was compared by using the Friedman–Nemenyi test. The results show that less complex architectures such as ResNet-50, ResNet-50r and DenseNet-121 were able to achieve better generalization with rankings of 1.53, 1.71 and 3.05 for the Matthew Correlation Coefficient, respectively, while MobileNet-v3 and CaiT obtained rankings of 3.72 and 5.0, respectively.