It is now becoming important for mobile cellular networks to accommodate all kinds of Internet of Things (IoT) communications. However, the contention-based random access and radio resource allocation used in traditional cellular networks, which are optimized mainly for human communications, cannot efficiently handle large-scale IoT communications. For this reason, standardization activities have emerged to serve IoT devices such as Cellular-IoT (C-IoT). However, few studies have been directed at evaluating the performance of C-IoT communications with periodic data transmissions, despite this being a common characteristic of many IoT communications. In this paper, we give the performance analysis results of mobile cellular networks supporting periodic C-IoT communications, focusing on the performance differences between LTE and Narrowband-IoT (NB-IoT) networks. To achieve this, we first construct an analysis model for end-to-end performance of both the control plane and data plane, including random access procedures, radio resource allocation, establishing bearers in the Evolved Packet Core network, and user-data transmissions. In addition, we include the impact of the immediate release of the radio resources proposed in 3GPP. Numerical evaluations show that NB-IoT can support more IoT devices than LTE, up to 8.7 times more, but imposes a significant delay in data transmissions. We also confirm that the immediate release of radio resources increases the network capacity by up to 17.7 times.