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Vehicle-to-vehicle (V2V) communication plays a pivotal role in intelligent transport systems (ITS) with cellular-vehicle to everything (C-V2X) and IEEE 802.11p being the two competing enabling technologies. This paper presents multi-dimensional discrete-time Markov chain (DTMC) based models to study the medium access control (MAC) layer performance of the IEEE 802.11p standard and C-V2X Mode 4, considering periodic cooperative awareness messages (CAMs) and event-driven decentralized environmental notification messages (DENMs). Closed-form solutions for the steady-state probabilities of the models are obtained, which are then utilized to derive expressions for several key performance metrics. Numerical results are provided to draw insights on the performance. In particular, a performance comparison between IEEE 802.11p and C-V2X Mode 4 in terms of the average delay, the collision probability, and the channel utilization is presented. The results show that IEEE 802.11p is superior in terms of average delay, whereas C-V2X Mode 4 excels in collision resolution. The paper also includes design insights on possible future MAC layer performance enhancements of both standards. [ABSTRACT FROM AUTHOR]