Hemingway and Eliot are both modernist writers. Literary modernism is a period that began in the late nineteenth century and continued into the early twentieth. Its peak was in the years following World War I, a traumatic transcontinental event that physically devastated and psychologically disillusioned the West in an entirely unprecedented way. Works of modernist authors reflect the pervasive sense of loss, disillusionment, and despair in the wake of the "Great War"; hence their emphasis on historical discontinuity and the alienation of humanity. Although many modernist authors tended to perceive the world as fragmented, others believed they could help counter that disintegration through their works.
Eliot's "The Waste Land" is one such example of that fragmentation. The poem is divided into five sections: "The Burial of the Dead," "A Game of Chess," "The Fire Sermon," "Death by Water," and "What the Thunder Said." Rather than asking, "What does this poem mean?" it is perhaps more helpful to consider, "What does this poem express?" The poem lives in our mouth and ears as much as it lives in the head. It is multivocal (meaning there are many speakers), and some critics have suggested that the poem is not coherent and was never meant to be: rather, it is "wild" in the way that the world after WWI is. Eliot draws on many of his predecessors—Shakespeare, Donne, and so on—and works to gather the shards of the literary tradition so that they now reflect the modern state of the world. "The Waste Land" is open to infinite interpretations and gets messier the more you try to place a single meaning onto it.
By contrast, Hemingway's The Sun Also Rises contains a much clearer narrative and, because of the sparsity of Hemingway's prose, is relatively easy to understand. Hemingway is deceptive, however; he practices the "iceberg theory," which means that ten percent of what he writes is "above the surface" (the words written on the page), and the other ninety percent is "below the surface" (between the lines, arising as the reader infers and interprets). The novel is a Roman à clef (a novel about real events, covered with a veil of fiction). One of Hemingway's original titles for the novel was The Lost Generation, a phrase often used to describe people who came of age during and just after WWI. The novel grapples with masculinity and the problem of people who are unable to communicate with one another. The characters in this novel have a hard time speaking frankly and honestly, and this "crisis of communication" prevents authentic relationships from developing.
To say The Sun Also Rises is Hemingway's own version of "The Waste Land" oversimplifies both works. TSAR is an exploration of how war changes the people who experienced it firsthand, marking veterans as "different" from civilians. It also questions masculinity (Jake Barnes, the protagonist, is impotent), life as an expatriate, and the emptiness of language. Hemingway is in many ways exploring himself in this novel. "The Waste Land," on the other hand, is a far messier work. Eliot himself does not appear in his poem as obviously as Hemingway appears in his novel. The poem makes obscure references to religion, history, literature, and mythology, and is almost intended to make the reader dizzy in their confusion as allusions layer on top of allusions. It grapples with modernism as an entire historical moment, while TSAR uses people for its study of that same moment. In other words, Eliot is taking a sweeping global view, while Hemingway is narrowing in on modern man in his current condition.
A comparison of the titles of the works reveals optimism in one and bleakness in the other. The guarantee that the sun will rise tomorrow helps alleviate the despair we feel when the sun sets. "The Waste Land," on the other hand, offers us no such hope, at least not in the title. "These fragments I have shored against my ruins," reads one of the poem's final lines, meaning this speaker has salvaged the fragments of what is left of a broken world in the hope of reassembling them into something new, something healed.
While both works are modernist, the project of each author is quite different. Ultimately, while the texts can be positioned in conversation with one another, it is reductionist to call Hemingway's The Sun Also Rises a different version of "The Waste Land." They each stand separately, equally impressive and equally powerful.