The innovation of reusable rockets holds the potential to revolutionize both Mars scientific exploration and commercial tourism. Thus, this paper aims to indicate the most promising propulsion system for the Mars mission. While SpaceX proposed the cryogenic liquid rocket Starship to achieve Mars colonization by 2050, the viable nuclear thermal propulsion has been outlined by rocketry experts for space travel. This paper surveys the current state-of-the-art of both popular propulsion systems, indicating their advantages and disadvantages. Methods to increase the delivery and cost efficiency are also offered, including on-orbit refueling for cryogenic liquid rockets and various nuclear core variants for nuclear thermal rockets. Subsequently, their comparative analysis is delivered in the discussion, focusing on their transportation efficiency and cost efficiency for future mass missions. With faster travel, greater payload, and reduced propellant consumption, nuclear thermal propulsion has shown to be a brighter prospect and potential than cryogenic liquid rocket. Nevertheless, the author believes a new class of bimodal nuclear thermal electric propulsion system is the most promising option, combining the merits and complementing drawbacks of cryogenic liquid propulsion, nuclear thermal propulsion, and nuclear electric propulsion.