Mobile Edge Cloud (MEC) is paving the way for 5G networks with respect to latency and computation offloading. To support user mobility, a MEC application should be migrated from one MEC server to another MEC server, which is in close proximity to users. Providing low migration time and low downtime is one of the critical challenges in MEC. Prior studies mainly focused on the service migration in data centers where only the downtime is taken into account. Meanwhile, the total migration time in MEC significantly influences the service latency due to the user's mobility. In this paper, we present a comparative measurement study on service migration in MEC. The evaluation results, which are obtained from commercial edge servers, show the infeasibility of the investigated migration approaches. Even though containerization is undoubtedly a lightweight virtualization technology, it is not mature enough to support the service migration in MEC. Specifically, both VM migration and container migration introduce high migration time, and subsequently result in service degradation for latency-sensitive applications in MEC.