Self-supervised learning (SSL) in computer vision has shown its potential to reduce reliance on labeled data. However, most studies focused on balanced, large, broad-domain datasets like ImageNet, whereas, in real-world medical applications, dataset size is typically limited. This study compares the performance of SSL versus supervised learning (SL) on small, imbalanced medical imaging datasets. We experimented with four binary classification tasks: age prediction and diagnosis of Alzheimer's disease from brain magnetic resonance imaging scans, pneumonia from chest radiograms, and retinal diseases associated with choroidal neovascularization from optical coherence tomography with a mean size of training sets of 843 images, 771 images, 1,214 images, and 33,484 images, respectively. We tested various combinations of label availability and class frequency distribution, repeating the training with different random seeds to assess result uncertainty. In most experiments involving small training sets, SL outperformed the selected SSL paradigms, even when a limited portion of labeled data was available. Our findings highlight the importance of carefully selecting learning paradigms based on specific application requirements, which are influenced by factors such as training set size, label availability, and class frequency distribution.