(1) Background: Detecting people and technical objects in various situations, such as natural disasters and warfare, is critical to search and rescue operations and the safety of civilians. A fast and accurate detection of people and equipment can significantly increase the effectiveness of search and rescue missions and provide timely assistance to people. Computer vision and deep learning technologies play a key role in detecting the required objects due to their ability to analyze big volumes of visual data in real-time. (2) Methods: The performance of the neural networks such as You Only Look Once (YOLO) v4-v8, Faster R-CNN, Single Shot MultiBox Detector (SSD), and EfficientDet has been analyzed using COCO2017, SARD, SeaDronesSee, and VisDrone2019 datasets. The main metrics for comparison were mAP, Precision, Recall, F1-Score, and the ability of the neural network to work in real-time. (3) Results: The most important metrics for evaluating the efficiency and performance of models for a given task are accuracy (mAP), F1-Score, and processing speed (FPS). These metrics allow us to evaluate both the accuracy of object recognition and the ability to use the models in real-world environments where high processing speed is important. (4) Conclusion: Although different neural networks perform better on certain types of metrics, YOLO outperforms them on all metrics, showing the best results of mAP-0.88, F1-0.88, and FPS-48, so the focus was on these models.