Both of these poems are dramatic monologues which means that they are written in the first person and in both poems we get to see into the mind of a murderer. Both poems contain a character created by the poet, the lover and the Duke, and we get to witness their motivations for killing.
The Duke kills his wife because he feels that she is not appreciative of his status and possibly she has been unfaithful (although there is no proof of this.) The lover also feels jealous of other men; 'vainer ties dissever' and feels that this is the only way that he can fully possess her.
Both poems have a similar tone in that there is no remorse felt by either man for what they have done. In fact Porphria's lover calls her murder 'A thing to do' and seems to act on a whim to preserve this perfect moment between them.
The poems are slightly different in the time period they are set as the Duke is probably 16th century whereas the other poem is more contemporary.