Virtualization is a key building block of next‐generation mobile networks. It can be implemented through two main approaches: traditional virtual machines (VMs) and lighter‐weight containers. Our objective in this paper is to compare these approaches and study the power consumption they are associated with. To this end, we perform a large set of real‐world measurements, using both synthetic workloads and real‐world applications, and use them to model the relationship between the resource usage of the hosted application and the power consumption of both VMs and containers hosting it. We find that containers incur substantially lower power consumption than VMs and that such consumption increases more slowly with the application load.