This study presents two new approaches based on Weighted Contourlet Parametric (WCP) images for the classification of breast tumors from B-mode ultrasound images. The Rician Inverse Gaussian (RiIG) distribution is considered for modeling the statistics of ultrasound images in the Contourlet transform domain. The WCP images are obtained by weighting the RiIG modeled Contourlet sub-band coefficient images. In the feature-based approach, various geometrical, statistical, and texture features are shown to have low ANOVA p-value, thus indicating a good capacity for class discrimination. Using three publicly available datasets (Mendeley, UDIAT, and BUSI), it is shown that the classical feature-based approach can yield more than 97% accuracy across the datasets for breast tumor classification using WCP images while the custom-made convolutional neural network (CNN) can deliver more than 98% accuracy, sensitivity, specificity, NPV, and PPV values utilizing the same WCP images. Both methods provide superior classification performance, better than those of several existing techniques on the same datasets.