Different poems appeal in different ways and some are not really comparable. I wouldn't attempt to compare The Love Song of J. Alfred Prufrock by T.S. Eliot - a poem I enjoyed at the age of seventeen - with Milton's Lycidas, which I had to study (and also enjoyed) when I was sixteen. But examiners love to make people 'compare', and so I suppose it is a valid exercise to look in a critical way at two different poet's rendering of the same general theme.
Here is a request for help with this that I received
"I am a GCSE student taking english literature. I have been asked to write an essay comparing the two poems A Poison Tree by William Blake and You in Anger by James Reeves. I would greatly appreciate any ideas or tips you could give me for my essay. Thank-you."
When you compare any two pieces of writing (or music or painting or drama or cake), you are going to be looking at similarities and differences. So here are some things you can look for in poetry.
Poems are always about something, even if it's not immediately obvious. Dylan Thomas starts one of his poems with the line: "In the beginning was the three pointed star," and goes on to
Part of the rhythm is the effect of having lines of a certain length. In the sonnet form these are predetermined - as is the number of lines.
I heard a rap poem on the radio recently. The poet was a young woman writing about the fairy tale Rapunzel. "Rap-punzel, Rap-punzel, let down your hair" was the refrain. It was very effective.