How did the way Fitzgerald used the symbol of class and society compare to other works of literature?
This is a rather open-ended question, as you didn't limit the comparative literature to the same time period as Fitzgerald's Gatsby; so I'm going to pick several other works of literary merit with which to compare, regardless of when and where they were written.
Fitzgerald was one of the disillusioned writers and artists, known as the Lost Generation, who left America and went to Paris. As a group, they found America to be too oppressive and unrefined about a whole host of things after World War I. Fitzgerald, both because of some incidents in his own life and as part of this movement, was unhappy with America's excessive hunger for money and class and entertainment as a way of forgetting the horrors of a world war. The Great Gatsby is a reflection of all those sentiments. To him, wealth and society (class) were not synonymous--having money was no guarantee of class, and vice versa.
Other writers have dealt with those same two issues but in vastly different ways. The most obvious example is Jane Austen's Pride and Prejudice. Here, Austen makes the exact same point as Fitzgerald--that money and class are not an exclusive pairing. Mr. Darcy and Elizabeth Bennett painfully discover that presuming money is an indicator of class is wrongheaded. This approach is much lighter and more ironically humorous than Fitzgerald's, but the point is the same.
How about John Steinbeck's The Grapes of Wrath, in which those who have money and class are nameless, cruel entities and those who are poor become the primary sympathetic characters in the narrative. William Randolph Hearst, the publishing mogul who owned vast holdings in California, was never named outright in the novel; yet we know each of the Joads and every nuance of their impoverished, desperate plight. Steinbeck's commentary is the same, as he creates literal dirt poor and displaced farmers who are helpful and kind and sacrificial in the face of wealthy profiteers who treat their workers as less than human.
Plenty of other works fit this thematic model, and all tend to make the same case. Unlike Austen's rather light-hearted social commentary and Steinbeck's homage to the working poor, Fitzgerald's work has an element of disillusionment that the others do not. Gatsby is the character who lives it out and discovers the hard way that one cannot earn enough money to buy either social equality or happiness.
I agree that the nature of the question is so open that anything can be tossed into the fray. With that in mind, I think that there could be a good comparison between Fitzgerald's treatment of class and society and Flaubert's treatment in Madame Bovary. Both narratives feature protagonists who wish to enter a world that is closed off to them. Bovary barters off and spends everything she has to pursue dreams in a world that is not meant for her. Gatsby does much of the same. Additionally, the construction of these worlds shows a great deal of cruelty of the people within it. The Jordan Bakers, Tom and Daisy Buchanans of the world can be contrasted with the Rodolphes and Leons. All of them see people as a means to an end and not an end in their own right. They also use the protagonists for their own end. Also, both protagonists end up being crushed by the weight of their own dreams that are rooted in social acceptance and material advancement. In this light, there is a great deal of challenge for both and a statement that the world of class and wealth can be a brutal one for those whose dreams cannot be achieved.