What causes Titan a moon to have a denser atmosphere than that of a Mars? I'm wondering about Mars and Titan. If Mars is larger than Titan how come it lost most of its atmosphere? Mars also has a magnetic field while Titan doesn't. Yet Titans atmospheric pressure on the surface is a whopping 1.5 times that of Earth's. 

Question: What causes Mars not to have much of an atmosphere, but Titan does?
Mars and Titan differ markedly in distance from the Sun, composition, and possibly geological activity.

Titan is about 6.3 times as remote from the Sun as is Mars, which means Titan receives about 1/40th solar radiation that Mars does, with about the same reduction in solar wind. Mars' small size coupled with its much closer proximity to the Sun allowed the solar wind to rip much of Mars' atmosphere away. Despite the marked differences between the atmospheres of Venus, Earth, and Mars, the atmospheric loss rates (in terms of mass loss per unit time) from these three planets are estimated to be about the same. This rate represents a pittance for Venus' very large atmosphere of Venus, a small amount for Earth's somewhat large atmosphere, but a huge proportional loss rate for Mars. Titan is spared to some extent.

Mar's average density is 3.93 g/cm3. Mars is a terrestrial planet. Titan's average density is less than half that, 1.88 g/cm3. Titan is an icy moon: some rock, but a lot of volatiles. There's a lot of ammonia mixed in with the water ice (and possibly liquid water deep down, if Titan's core is warm). Some hypothesize that Titan regenerates its atmosphere via releases of ammonia. Sunlight splits ammonia near the top of Titan's atmosphere into hydrogen and nitrogen. The hydrogen escapes, but not the nitrogen.

Finally, Mars is most likely dead geologically. It's covered with craters that may date back to the Late Heavy Bombardment. Titan exhibits some signs of being somewhat active, geologically. It too has craters, but it's not as plastered with them as is Mars. It's mountains appear to be younger, at least according to some. The geological activity may help to regenerate Titan's atmosphere.