Neural network pruning and quantization techniques are almost as old as neural networks themselves. However, to date, only ad-hoc comparisons between the two have been published. In this paper, we set out to answer the question of which is better: neural network quantization or pruning? By answering this question, we hope to inform design decisions made on neural network hardware going forward. We provide an extensive comparison between the two techniques for compressing deep neural networks. First, we give an analytical comparison of expected quantization and pruning error for general data distributions.Then, we provide lower and upper bounds for the per-layer pruning and quantization error in trained networks and compare these to empirical error after optimization.Finally, we provide an extensive experimental comparison for training 8 large-scale models trained on 3 tasks and provide insights into the representations learned during fine-tuning with quantization and pruning in the loop.Our results show that in most cases quantization outperforms pruning. Only in some scenarios with a very high compression ratio, compression might be beneficial from an accuracy standpoint.