5G New Radio (NR) Release 15 has been specified in June 2018. It introduces numerous changes and potential improvements for physical layer data transmissions, although only point-to-point (PTP) communications are considered. In order to use physical data channels such as the Physical Downlink Shared Channel (PDSCH), it is essential to guarantee a successful transmission of control information via the Physical Downlink Control Channel (PDCCH). Taking into account these two aspects, in this paper, we first analyze the PDCCH processing chain in NR PTP as well as in the state-of-the-art Long Term Evolution (LTE) point-to-multipoint (PTM) solution, i.e., evolved Multimedia Broadcast Multicast Service (eMBMS). Then, via link level simulations, we compare the performance of the two technologies, observing the Bit/Block Error Rate (BER/BLER) for various scenarios. The objective is to identify the performance gap brought by physical layer changes in NR PDCCH as well as provide insightful guidelines on the control channel configuration towards NR PTM scenarios.