Electroluminescence (EL) imaging is a useful modality for the inspection of photovoltaic (PV) modules. EL images provide high spatial resolution, which makes it possible to detect even finest defects on the surface of PV modules. However, the analysis of EL images is typically a manual process that is expensive, time-consuming, and requires expert knowledge of many different types of defects. In this work, we investigate two approaches for automatic detection of such defects in a single image of a PV cell. The approaches differ in their hardware requirements, which are dictated by their respective application scenarios. The more hardware-efficient approach is based on hand-crafted features that are classified in a Support Vector Machine (SVM). To obtain a strong performance, we investigate and compare various processing variants. The more hardware-demanding approach uses an end-to-end deep Convolutional Neural Network (CNN) that runs on a Graphics Processing Unit (GPU). Both approaches are trained on 1968 cells extracted from high resolution EL intensity images of mono- and polycrystalline PV modules. The CNN is more accurate, and reaches an average accuracy of 88.42%. The SVM achieves a slightly lower average accuracy of 82.44%, but can run on arbitrary hardware. Both automated approaches make continuous, highly accurate monitoring of PV cells feasible.