Hmmmm, this would be the difference of prominent literature fueled by prosperity versus that fueled by poverty or depression. What an interesting idea! Originally, I thought the mere presence of F. Scott Fitzgerald in the mix would make me side with 1920s literature. Then I thought about Steinbeck, and although I'm not a big fan, I can't deny how much he did for the plight of the migrant worker and the general poor of the 1930s. Now I'm stumped. I guess my final thoughts would have to include how both prosperity AND povery can both inspire equally appreciative literature ANYWHERE, not just here in the United States. In my opinion, it's coasting into the mundane that promotes bland writing.
This time period is literature is also associated with the rise of Modernism. Authors were challenging the established precepts of story or poem construction and trying new things stylistically -- for example the unresolved ending that is more open to interpretation in a short story or wide use of free verse in poetry. The themes presented in fiction and poetry reflected what the author's saw as more modern times and more modern issues.
Writers are influenced by the time in which they write, but they are also influenced by the surrounding area. Writers of north in the 20's and 30's may not have felt as strongly or at all as writers in the south about certain issues. You're dealing with WWI, racism, the Depression, the booze issue and the illegal bars all over the north, the flappers, gang activity...not all of this would effect regional writers in different areas of the country.
As mentioned above, you also have the expatriots who would have been affected by incidents in the countries from which they wrote in addition to the current events they would have heard about at home.
I think one can argue there was a greater environmental influence in the 1920s and 30s than in other decades, perhaps, but it's very difficult to say with any accuracy whether one group was affected more than another.
Consider the "expatriates"--American authors who more or less quit the society and wrote in Europe during those decades--were strongly influenced by both the American materialist environment, influenced to leave that is, and by the European artistic and creative environment which nurtured and encouraged them to write as much as they did. Many of them were in Paris during that time, a very pacifist, anti-war society, which, I would imagine, is reflected in their writings to some degree.
Writers are always influenced by the times in which they write--and the more extreme the times, the more pronounced the impact. In the case of these two decades, I would think the '30s would generally be more impactful across the board than the '20s. Nearly everyone felt the pain and suffering and want of the Great Depression; the Roaring Twenties were a real, nationwide reaction to World War I, but it was not necessarily seen as a negative by everyone. Only those who recognized the excessiveness and carelessness of the times (as Fitzgerald did) would have been so impacted by the '20s.
I assume you are referring to American literature? If so, then definitely one approach would be to compare and contrast the differences between iconic writers of the time and see how the themes prevalent historically impacted their fiction. Fitzgerald and Steinbeck would be great places to start - easily accessible fiction clearly set in a definite historical context that impacts the works of these authors greatly.
This is a fairly wide open question. I think that it will be nearly impossible to answer the question fully in this forum. Yet, I do believe that there can be some initial thoughts suggested. There is an undeniable emphasis on material conditions and environment impacting the construction of literature in both decades. If we examined literature and the construction of literature in the 1920s, much is dependent on how the literature of the Europeans contrasted with that of the Americans. The former saw their nations crippled by the results of the First World War, while the latter saw itself immersed in the Jazz Age and the notion of materialism that gripped the nation. In this setting, we can see how environment impacts the construction of literature. Specific examples would be contrasting the work of Fitzgerald and Yeats, for instance. The same analysis can be applied to the 1930s, where the Great Depression impacted the world over and the literature that came out of it. When Steinbeck, for example, writes in the name of the dispossessed, he does so to highlight the role of environment on writers of this time period.