Convolutional Neural Networks (CNNs) have demonstrated remarkable success in image classification tasks; however, the choice between designing a custom CNN from scratch and employing established pre-trained architectures remains an important practical consideration. In this work, we present a comparative analysis of a custom-designed CNN and several widely used deep learning architectures, including VGG-16, ResNet-50, and MobileNet, for an image classification task. The custom CNN is developed and trained from scratch, while the popular architectures are employed using transfer learning under identical experimental settings. All models are evaluated using standard performance metrics such as accuracy, precision, recall, and F1-score. Experimental results show that pre-trained CNN architectures consistently outperform the custom CNN in terms of classification accuracy and convergence speed, particularly when training data is limited. However, the custom CNN demonstrates competitive performance with significantly fewer parameters and reduced computational complexity. This study highlights the trade-offs between model complexity, performance, and computational efficiency, and provides practical insights into selecting appropriate CNN architectures for image classification problems.