Though both the poems are anti-war poems there are some clear differences in their theme, structures and way of conveying messages.

In “A Doctor’s Journal Entry” the poet has depicted the devastation caused by the first atomic explosion on Japan. It is his protest against atomic warfare and such inhuman mass killings. But, in “Small Pain in My Chest”, the protest is against war at large.

Again, if we see it in terms of the point of view, Vikram Seth shows everything from a common man, a doctor who is the victim. But, Michael Mack shows it all from the angle of a soldier who speaks of his thoughts and feelings by himself.

When it comes to structures and narration, Small Pain follows a stanza pattern and a rhyme scheme, while Doctor’s Journal Entry is in a journal pattern with no rhyme or stanza division. In the former, the victim, the soldier is not the narrator, but we are seeing him from a different narrator’s view. On the other hand, In Seth’s poem the victim himself narrates it all.

Vikram seth employs symbols of silence and nakedness in his poem, while Mack has employed a sharp irony in showing the soldier’s pain as “a small pain in his chest”.
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I have also answered a question on the similarity of the two poems. You may read it here: Show how Small Pain in My Chest is similar to A Doctor’s Journal Entry.