Various Computer Aided Diagnosis (CAD) systems have been developed that characterize thyroid nodules using the features extracted from the B-mode ultrasound images and Shear Wave Elastography images (SWE). These features, however, are not perfect predictors of malignancy. In other domains, deep learning techniques such as Convolutional Neural Networks (CNNs) have outperformed conventional feature extraction based machine learning approaches. In general, fully trained CNNs require substantial volumes of data, motivating several efforts to use transfer learning with pre-trained CNNs. In this context, we sought to compare the performance of conventional feature extraction, fully trained CNNs, and transfer learning based, pre-trained CNNs for the detection of thyroid malignancy from ultrasound images. We compared these approaches applied to a data set of 964 B-mode and SWE images from 165 patients. The data were divided into 80% training/validation and 20% testing data. The highest accuracies achieved on the testing data for the conventional feature extraction, fully trained CNN, and pre-trained CNN were 0.80, 0.75, and 0.83 respectively. In this application, classification using a pre-trained network yielded the best performance, potentially due to the relatively limited sample size and sub-optimal architecture for the fully trained CNN.