The most obvious common theme is that of death. In "Funeral Blues," a loved one has died, and as a result, the author's entire world has stopped--they are devastated. In "Do Not Go Gentle into That Good Night," a loved one of the author's also faces death. Thomas' father is on his deathbed, and Thomas pleads with him to die with vigor, fighting against it the entire time. So, death, especially of a loved one, is a very prevalent main theme.
Another possible common theme the poems share is love. It is very obvious that the authors loved the subjects of the poems. In "Funeral Blues," Auden's love is described poetically:
"He is my North, my South, my East and West/My working week and my Sunday-rest/My moon, my midnight, my talk my song."
Auden's love for the deceased was all-encompassing, and that definitely comes through. Thomas' love for his father can be seen all throughout the poem as he wants his father to die a dignified death, and begs his father at the end, "Curse, bless, me now with your fierce tears, I pray," making a personal connection, wanting one last moment with his father. So, a discussion of the poets' love for the subjects is another common theme.
Hopefully those ideas help you to get started; good luck!