In this paper, we develop physics-based performance models of plasmonic single waveguide (SWG) and parallel-plate waveguide (PPWG) interconnects using multilayer graphene (MLG) stack. While the SWG supports transverse magnetic plasmon modes, in the PPWG geometry, quasi-transverse electromagnetic modes emerge as the eigen modes. Using complex dynamical conductivity of MLG obtained from the Kubo formalism, we quantify the impact of the number of layers, electrostatic screening length, and the electrochemical potential on the transport characteristics of plasmon modes up to the terahertz frequencies (< 2 THz). Analytical models of the frequency-dependent distortion and attenuation of a propagating THz Gaussian pulse through the plasmonic interconnect are derived. While PPWG interconnects offer near dispersionless transmission, they have higher signal attenuation compared to the SWG interconnects implying a higher energy-per-bit for PPWG interconnects. We show that the bitrate density of PPWG interconnects is (1-2) orders of magnitude higher than that of electrical interconnects for length scales up to 1 mm. However, the energy dissipation of plasmonic interconnects increases exponentially with interconnect length. As such, the optimal length scales for plasmonic interconnects are several tens to a few hundreds of micrometers. By establishing a clear link between the device- and material-level parameters with the system-level performance, we show that plasmonic interconnects outperform copper interconnects at near-short and semi-global length scales.