Federated learning is a distributed machine learning approach for computing models over data collected by edge devices. Most importantly, the data itself is not collected centrally, but a master-worker architecture is applied where a master node performs aggregation and the edge devices are the workers, not unlike the parameter server approach. Gossip learning also assumes that the data remains at the edge devices, but it requires no aggregation server or any central component. In this empirical study, we present a thorough comparison of the two approaches. We examine the aggregated cost of machine learning in both cases, considering also a compression technique applicable in both approaches. We apply a real churn trace as well collected over mobile phones, and we also experiment with different distributions of the training data over the devices. Surprisingly, gossip learning actually outperforms federated learning in all the scenarios where the training data are distributed uniformly over the nodes, and it performs comparably to federated learning overall.