Chronic obstructive pulmonary disease (COPD) is a leading cause of global mortality, often remaining undetected until irreversible lung damage occurs. Leveraging advancements in AI and acoustic diagnostics, in this study, we compare the performance of deep learning models for COPD detection using respiratory sound data. Mel spectrogram and Mel-frequency cepstral coefficients were extracted from a publicly available dataset comprising crackle sounds from COPD patients and normal breath sounds. We evaluated standalone convolutional neural network (CNN) models (Residual Network, InceptionV3, and VGG16), a long short-term memory (LSTM) model, and hybrid CNN-LSTM and LSTM-CNN architectures. The LSTM outperformed standalone CNNs, achieving 94% accuracy, 93% precision, 99% recall, and an F1-score of 0.96, demonstrating its effectiveness in modeling temporal dependencies. The VGG16-LSTM achieved the highest performance, with 97.1% accuracy and 99% recall, highlighting the advantage of combining spatial feature extraction with temporal learning. However, several limitations should be acknowledged. The study relies on a single publicly available dataset, lacks real-world clinical validation, and adopts a binary classification framework that does not account for COPD severity staging. Future work will focus on multi-dataset validation, severity-graded classification, and the integration of edge-deployable models into wearable acoustic sensing platforms for real-time clinical application. These results underscore the potential of advanced deep learning models for accurate and accessible COPD diagnosis and support the development of next-generation acoustic sensors with enhanced sensitivity, improved signal-to-noise ratios, and integrated processing capabilities.