Pulmonary embolism (PE) represents a thrombus (“blood clot”), usually originating from a lower extremity vein, that travels to the blood vessels in the lung, causing vascular obstruction and in some patients, death. This disorder is commonly diagnosed using CT pulmonary angiography (CTPA). Deep learning holds great promise for the computer-aided CTPA diagnosis (CAD) of PE. However, numerous competing methods for a given task in the deep learning literature exist, causing great confusion regarding the development of a CAD PE system. To address this confusion, we present a comprehensive analysis of competing deep learning methods applicable to PE diagnosis using CTPA at the both image and exam levels. At the image level, we compare convolutional neural networks (CNNs) with vision transformers, and contrast self-supervised learning (SSL) with supervised learning, followed by an evaluation of transfer learning compared with training from scratch. At the exam level, we focus on comparing conventional classification (CC) with multiple instance learning (MIL). Our extensive experiments consistently show: (1) transfer learning consistently boosts performance despite differences between natural images and CT scans, (2) transfer learning with SSL surpasses its supervised counterparts; (3) CNNs outperform vision transformers, which otherwise show satisfactory performance; and (4) CC is, surprisingly, superior to MIL. Compared with the state of the art, our optimal approach provides an AUC gain of 0.2% and 1.05% for image-level and exam-level, respectively.