How can we compare Eliot to Joyce, to Orwell, and to Beckett?

Compare Eliot to Joyce

Eliot and Joyce compare favorably in that each was innovative and experimental, bringing new styles or forms to English literature. They contrast in that Eliot was prolific in universal themes, writing extensively in criticism, drama and poetry, while Joyce produced a small body of work in short stories, novels and poetry, writing in an expository manner on highly personal themes that he sought to universalize. Another point of contrast is that Eliot was respected by publishers whereas Joyce battled with publishers. The reasons behind this difference relating to publishers is primarily (though perhaps not exclusively) that Eliot was an elegant writer who, according to his literary aesthetic, bent classical literature to serve a modern purpose, whereas Joyce was profane to the point of fighting court battles against profanity charges.

Compare Eliot to Orwell

Eliot and Orwell employed different writing styles. While both were essayists (with Eliot also being a critic, dramatist and poet contrasted with Orwell also being a novelist), Eliot based his literary style on classical literary trends while Orwell based his literary style on modern trends and futuristic science fiction.

Eliot and Orwell compare favorably in that some of each man's work had worldwide impact for the universal themes written of by each. Eliot's works "The Love Song of J. Alfred Prufrock" and The Waste Land are read, at least in part, on every continent and by virtually every student of English literature. The same is true for Orwell's two novels Animal Farm and Nineteen Eighty-Four. Another point of comparison is that both, in different ways, address the universal theme of the destruction and deterioration of contemporary society. While both apply the realization of this theme of deterioration to individuals, Eliot takes the theme one step further and applies it to the simultaneous deterioration of the land under our feet:    

I. The Burial of the Dead
April is the cruellest month, breeding
Lilacs out of the dead land, mixing
Memory and desire, stirring
Dull roots with spring rain. (The Waste Land)

Compare Eliot and Beckett

Eliot and Beckett have more differences than similarities, although they do have some aspects of thought and work in common. While Eliot was a Modernist and Beckett the first post-modernist, both men shared an indisputable sense of the absurd. Beckett's sense of the absurd built his reputation as he exclusively wrote fictional works of the absurd, such as Waiting for Godot (1954). Eliot's sense of the absurd--though he was a Modernist still clinging to the hope of an orderly world--is apparent in both The Waste Land and "Prufrock":

Let us go, through certain half-deserted streets,
The muttering retreats
Of restless nights in one-night cheap hotels
And sawdust restaurants with oyster-shells:
Streets that follow like a tedious argument
Of insidious intent
To lead you to an overwhelming question...  10
Oh, do not ask, "What is it?" ("The Love Song of Alfred J. Prufrock")

Both men were deep thinkers and were prolific across a wide range of fiction, criticism and drama (Beckett, though a renowned critic, is known mostly for his fiction and drama). A difference between them is that Eliot wrote in English whereas Beckett wrote in English and French.

According to Eliot's literary aesthetic, art succeeds in communicating the inner thoughts of humankind through external reality. In contrast, according to Beckett's aesthetic, even art fails to communicate the inner voice of humanity into external reality. For Beckett, only the inner experience has any reality while, in contrast, for Eliot, both the inner experience and the outer experience have reality; in fact, the inner experience can bear upon the external reality to alter it under the force of art.

VLADIMIR:
Sometimes I feel it coming all the same. Then I go all queer. (He takes off his hat, peers inside it, feels about inside it, shakes it, puts it on again.) How shall I say? Relieved and at the same time . . . (he searches for the word) . . . appalled. (With emphasis.) AP-PALLED. (He takes off his hat again, peers inside it.) Funny. (He knocks on the crown as though to dislodge a foreign body, peers into it again, puts it on again.) Nothing to be done. (Beckett, Waiting for Gordot I)