This is an interesting question! Both poems juxtapose Greek grandeur against the mundane realities of everyday life. Both are also what are known as ekphrastic poems. Ekphrastic poems are about or involve a work of art.
In "Musée des Beaux Arts," the speaker gazes at and comments on a Breughel painting called Icarus, arguing that it captures a truth about human existence. This painting depicts the Greek myth of Icarus, a lad who is taught by his father to fly, but soars too high. The sun melts his wings, and he plunges into the sea and drowns. Icarus is often seen as representing the artist or visionary, the person who risks everything to try to soar towards something that might destroy him, the person who tries to do more than the common person. Breughel's painting, Auden says, reveals the truth that nobody cares about the suffering of people who strive to reach the stars. The painting shows that children go on with their skating, and a ship floats placidly by, and
the ploughman may
Have heard the splash, the forsaken cry,
But for him it was not an important failure . . .
The world, in other words, really doesn't really care about our personal agonies.
In "On Seeing the Elgin Marbles," Keats comments on a visit to see these famous bas-reliefs that have recently arrived in England from Greece. To him, they represent a high artistic achievement that offers hints or glimpses at a "shadow of a magnitude," or a higher plane of existence that we ordinary mortals can only soar towards but never achieve. Looking at these marbles brings a "feud" and a "dizzy pain" into his heart, for he feels a mingling of their majesty with their damage by time. The experience
mingles Grecian grandeur with the rude
Wasting of old time . . .
Just as Breughel's painting shows a mixture of glorious and mundane, the Elgin marbles themselves are both glorious and damaged by the mundane passage of time. Art shows that the high and the low sit side by side.