Purpose: Metastases are the most common neoplasm in the adult brain. In order to initiate the treatment, an extensive diagnostic workup is usually required. Radiomics is a discipline aimed at transforming visual data in radiological images into reliable diagnostic information. We aimed to examine the capability of deep learning methods to classify the origin of metastatic lesions in brain MRIs and compare the deep Convolutional Neural Network (CNN) methods with image texture based features. Methods: One hundred forty three patients with 157 metastatic brain tumors were included in the study. The statistical and texture based image features were extracted from metastatic tumors after manual segmentation process. Three powerful pre-trained CNN architectures and the texture-based features on both 2D and 3D tumor images were used to differentiate lung and breast metastases. Ten-fold cross-validation was used for evaluation. Accuracy, precision, recall, and area under curve (AUC) metrics were calculated to analyze the diagnostic performance. Results: The texture-based image features on 3D volumes achieved better discrimination results than 2D image features. The overall performance of CNN architectures with 3D inputs was higher than the texture-based features. Xception architecture, with 3D volumes as input, yielded the highest accuracy (0.85) while the AUC value was 0.84. The AUC values of VGG19 and the InceptionV3 architectures were 0.82 and 0.81, respectively. Conclusion: CNNs achieved superior diagnostic performance in differentiating brain metastases from lung and breast malignancies than texture-based image features. Differentiation using 3D volumes as input exhibited a higher success rate than 2D sagittal images.