They both convey images of war. In Murder in the Cathedral, the image of war is between the divine and the regal--King Henry II vs. Thomas a Becket of Canterbury. The Bishop refuses to give in to what Henry wants, and so he is murdered in his own cathedral.
In Burial of the Dead, Eliot is referencing WWI, all the soldiers and other casualties who died and were buried during this time.
Of course, the months and settings are different for these images. Becket was murdered in 1170 and the play is set in December to further illustrate the cruelty of the act.
"Burial" is set in early spring..."April is the cruellest month"--wherein lies the irony of the birth and growth and regeneration of new life and the in the midst of it is all the death and dying of the soldiers.