The use of artificial intelligence algorithms (AI) has gained importance for dental applications in recent years. Analyzing AI information from different sensor data such as images or panoramic radiographs (panoramic X-rays) can help to improve medical decisions and achieve early diagnosis of different dental pathologies. In particular, the use of deep learning (DL) techniques based on convolutional neural networks (CNNs) has obtained promising results in dental applications based on images, in which approaches based on classification, detection, and segmentation are being studied with growing interest. However, there are still several challenges to be tackled, such as the data quality and quantity, the variability among categories, and the analysis of the possible bias and variance associated with each dataset distribution. This study aims to compare the performance of three deep learning object detection models—Faster R-CNN, YOLO V2, and SSD—using different ResNet architectures (ResNet-18, ResNet-50, and ResNet-101) as feature extractors for detecting and classifying third molar angles in panoramic X-rays according to Winter’s classification criterion. Each object detection architecture was trained, calibrated, validated, and tested with three different feature extraction CNNs which are ResNet-18, ResNet-50, and ResNet-101, which were the networks that best fit our dataset distribution. Based on such detection networks, we detect four different categories of angles in third molars using panoramic X-rays by using Winter’s classification criterion. This criterion characterizes the third molar’s position relative to the second molar’s longitudinal axis. The detected categories for the third molars are distoangular, vertical, mesioangular, and horizontal. For training, we used a total of 644 panoramic X-rays. The results obtained in the testing dataset reached up to 99% mean average accuracy performance, demonstrating the YOLOV2 obtained higher effectiveness in solving the third molar angle detection problem. These results demonstrate that the use of CNNs for object detection in panoramic radiographs represents a promising solution in dental applications.