In recent years, large strides have been taken in developing machine learning methods for dermatological applications, supported in part by the success of deep learning (DL). To date, diagnosing diseases from images is one of the most explored applications of DL within dermatology. Convolutional neural networks (ConvNets) are the most common (DL) method in medical imaging due to their training efficiency and accuracy, although they are often described as black boxes because of their limited explainability. One popular way to obtain insight into a ConvNet's decision mechanism is gradient class activation maps (Grad-CAM). A quantitative evaluation of the Grad-CAM explainability has been recently made possible by the release of DermXDB, a skin disease diagnosis explainability dataset which enables explainability benchmarking of ConvNet architectures. In this paper, we perform a literature review to identify the most common ConvNet architectures used for this task, and compare their Grad-CAM explanations with the explanation maps provided by DermXDB. We identified 11 architectures: DenseNet121, EfficientNet-B0, InceptionV3, InceptionResNetV2, MobileNet, MobileNetV2, NASNetMobile, ResNet50, ResNet50V2, VGG16, and Xception. We pre-trained all architectures on an clinical skin disease dataset, and fine-tuned them on a DermXDB subset. Validation results on the DermXDB holdout subset show an explainability F1 score of between 0.35-0.46, with Xception displaying the highest explainability performance. NASNetMobile reports the highest characteristic-level explainability sensitivity, despite it's mediocre diagnosis performance. These results highlight the importance of choosing the right architecture for the desired application and target market, underline need for additional explainability datasets, and further confirm the need for explainability benchmarking that relies on quantitative analyses.