One of the main causes of death for women globally is breast cancer, and better treatment results depend on early and precise identification. In order to classify breast cancer using medical imaging data, this study compares machine learning (ML) with deep learning (DL) approaches. Support Vector Machine (SVM), Random Forest (RF), and K-Nearest Neighbors (KNN) algorithms were used to classify the features that were retrieved using the Gray Level Co-occurrence Matrix (GLCM) in the machine learning technique. Among these techniques, the best accuracy attained was 85.17%. Using pre-trained architectures like VGG16 and ResNet16, convolutional layers were used in the DL technique to automatically extract features. These models performed quite well, with a maximum accuracy of 96.55%. The findings unequivocally show that deep learning models perform better than conventional machine learning methods that depend on manually created features since they can instantly learn intricate patterns from photos. This study supports the incorporation of DL into computer-aided diagnostic systems for clinical usage and emphasizes its potential to improve breast cancer diagnosis.