In my mind, the most initial level of comparison between both works is their critique of the American Dream. Sinclair's work critiques the "Horatio Alger" "rags to riches" mythology. This idea suggests that if individuals work hard enough and give their maximum effort, they can achieve the American Dream without examining the institutional complexities that makes this a statistical improbability. Jurgis believes that if he works harder, he can "make it." The reality proves to be quite different. In Fitzgerald's world, the idea of "the American Dream" turns out to be a nightmare in that Gatsby's hope of the self- made reality is something that ends up sealing his own doom and makes life a painful one, at best. For both narratives, the American Dream is one where there is a corroded core, one fraught with challenges and both institutional and social dynamics that makes happiness impossible. In both works, there is a critique of materialism within this pursuit of dreams. The materialism element is what makes Jurgis' life a brutal one, an existence that is trapped under the heel of capitalism. For Gatsby, the materialism existent in his world is one that drives his dreams and his pursuit. In the end, like Jurgis, materialism is something that ends up bringing more pain and suffering than anything liberating. In this, there is another mode of comparison between both works.
In The Jungle, Jurgis' makes his own life. As mentioned above, it is a sort of Horatio Alger story in that Juguis reaps what he sows. He loses his family and his home because he goes to jail.
In The Great Gatsby, Gatsby's dies due to an event unrelated to his life. Maybe you could call it Anti-Horatio Alger.
In The Great Gatsby, is materialism an end destination or only the means?