Unmanned aerial vehicles (UAVs) have recently received a significant interest to assist terrestrial wireless networks thanks to their strong line-of-sight links and flexible/instant deployment. However, UAVs' assistance is limited by their battery lifetime and wireless backhaul link capacity. At the expense of limited mobility, tethered UAVs (T-UAVs) can be a viable alternative to provide seamless service over a cable that simultaneously supplies power and data from a ground station (GS). Accordingly, this paper presents a comparative performance analysis of T-UAV and regular/untethered UAV (U-UAV)-assisted cellular traffic offloading from a geographical area that undergoes heavy traffic conditions. By using stochastic geometry tools, we first derive joint distance distributions between the hot-spot users, the terrestrial base station (TBS), and the UAV. To maximize the end-to-end signal-to-noise ratio, a user association policy is developed, and corresponding association regions are analytically identified. Then, the overall coverage probability of the U-UAV/T-UAV-assisted system is derived for given locations of the TBS and the U-UAV/T-UAV. Moreover, we analytically prove that optimal UAV location falls within a partial surface of the spherical cone centered at the GS. Numerical results show that T-UAV outperforms U-UAV given that sufficient GS locations accessibility and tether length are provided.