The detailed understanding of packet delays in modern wireless networks is crucial to optimize applications and protocols. We conducted high precision latency measurements in operational LTE and HSPA networks, deploying a hybrid approach of active probing and withe-box testing. It allowed us to separately assess the one-way delay contributions of the radio access network and the core network for both technologies. The results show that LTE outperforms HSPA in the case of medium to high data rates. However, due to differences in the radio access procedures, the HSPA uplink connection offers lower delay for specific traffic patterns. A comparison between our measurement results and the requirements for delay sensitive applications exhibits that LTE is not (yet) the generally preferable technology. Hence, further optimizations of the LTE scheduling and resource allocation policies are required to fully exhaust all feasible latency improvements.