You don't state whether or not you must compare this poem to another one that you have read in class, or if your assignment is to choose a poem with which to compare it. Since I am not familiar with what other poems you may have read, I can offer you some suggestions of poems that might be compared to this one in theme.
"The Shield of Achilles" describes the making of Achilles' shield as outlined by Homer in the Illiad. The god Hephaestus makes the shield, but he does not make it with peaceful, pastoral scenes as requested by Achilles' mother Thetis.
Out of the air a voice without a face
Proved by statistics that some cause was just
In tones as dry and level as the place:
No one was cheered and nothing was discussed;
Column by column in a cloud of dust
They marched away enduring a belief
Whose logic brought them, somewhere else, to grief.
Instead, Hephaestus creates a shield that depicts scenes of war. One interpretation of this poem is that it is an anti-war poem. Achilles is the fighter, but the shield's creation is effected by his mother and by Hephaestus, out of the control of Achilles. In this sense, Achilles is like a soldier who is sent to fight a war that is effected by powers other than himself.
So, a similar poem you can compare it to is one by e.e. cummings, which he calls XXX but commonly is referrred to by the first line:
i sing of Olaf glad and big
whose warmest heart recoiled at war:
a conscientious object-or
Another view of "The Shield of Achilles" that it expresses Auden's disillusionment with the modern world, a world in which the individual is impotent but the state is powerful.
If you like this interpretation, you can compare it to something by T. S. Eliot, such as The Hollow Men. Also, Sara Teasdale's poem "There Will Come Soft Rains" might work. These are both poems of disillusionment as well.
If you do not like these suggestions, ask yourself what YOUR interpretation of the poem is, and then try to find something similar in theme.
Here are some links below that might help you.