Ear recognition is an active research area in the biometrics community with the ultimate goal to recognize individuals effectively from ear images. Traditional ear recognition methods based on handcrafted features and conventional machine learning classifiers were the prominent techniques during the last two decades. Arguably, feature extraction is the crucial phase for the success of these methods due to the difficulty in designing robust features to cope with the variations in the given images. Currently, ear recognition research is shifting towards features extracted by Convolutional Neural Networks (CNNs), which have the ability to learn more specific features robust to the wide image variations and achieving state-of-the-art recognition performance. This paper presents and compares ear recognition models built with handcrafted and CNN features. First, we experiment with seven top performing handcrafted descriptors to extract the discriminating ear image features and then train Support Vector Machines (SVMs) on the extracted features to learn a suitable model. Second, we introduce four CNN based models using a variant of the AlexNet architecture. The experimental results on three ear datasets show the superior performance of the CNN based models by 22%. To further substantiate the comparison, we perform visualization of the handcrafted and CNN features using the t-distributed Stochastic Neighboring Embedding (t-SNE) visualization technique and the characteristics of features are discussed. Moreover, we conduct experiments to investigate the symmetry of the left and right ears and the obtained results on two datasets indicate the existence of a high degree of symmetry between the ears, while a fair degree of asymmetry also exists.