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Supporting parallel multi-priority data streams is vital for maintaining the quality of service (QoS) in vehicle-to-everything (V2X) communication. Hence, the European telecommunications standard institute (ETSI) has defined four packet types, with varying priority levels, to be used as broadcast packets in such communication. This paper studies the medium access control (MAC) layer performance of IEEE 802.11p and cellular-V2X (C-V2X) Mode 4 using discrete-time Markov chain (DTMC) based models, while considering parallel multi-priority data streams. The overall model consists of four queue models with their respective traffic generators, which are appropriately linked with the DTMCs modeling the MAC layer operations of IEEE 802.11p and C-V2X Mode 4. Closed-form solutions for the steady-state probabilities of the models are obtained, which are then utilized to derive expressions for key performance indicators at the MAC layer. Numerical results are provided to draw insights on the MAC layer performance of the two technologies. IEEE 802.11p is comparatively superior in average delay, and at maintaining fairness among multi-priority data streams, whereas C-V2X Mode 4 exhibits better collision resolution, which leads to its higher throughput. The paper also includes design insights on possible performance enhancements for future releases. [ABSTRACT FROM AUTHOR]