The traditional methods used by researchers when implementing breathing sounds classification systems involve two main steps - feature extraction and pattern classification. In recent years, the topic of interest in the field of breathing sound classification focuses on the use of deep neural networks, which have been proven to be effective for training large datasets. In this paper, we conducted a comparative study of three deep neural network architectures, the VGG16, ResNet-50, and GoogLeNet for breathing sounds classification. Digital recordings of cycle-based breathing sounds from the ICBHI database are processed to obtain gammatonegram images that are fed as an input to these three networks. The classification results, executed on the Google Colaboratory platform, indicated that these three networks yielded accuracies of 62.50%, 62.29%, and 63.69% respectively. Hence, the results provide initial evidence that GoogLeNet can significantly improve the accuracy and outperformed the VGG16 and Resnet-50 in our application.