There are two versions of this poem, one dating from 1859, and one from 1861. In both versions, the first stanza is very similar—the key difference here is that the earlier version has the "meek members" asleep, while in the second version, they "lie." The nuance here, we could argue, is that to sleep suggests passivity, being closed off to the world, while if the dead are only lying in this chamber, there is a possibility that their consciousness remains somehow within our reach.
This is an idea which is carried through into the second stanzas, which differ far more significantly between the two poems. In the first version of the poem, Dickinson describes the "ignorant" chatter of bees, birds and the breeze, all of which continue to exist happily without any awareness of what "sagacity perished here." In this version of the poem, then, we can see that the wisdom of those in the chambers is definitively beyond our reach: as they "sleep," they may as well have perished.
By contrast, in the second version of the poem, the continuity of those lying in the chambers is emphasized. The language Dickinson uses creates a semantic field of grandeur and importance: the years that continue to pass are "grand," and "diadems" and "doges" seemingly "surrender" to death in the same way that the sleepers have done. This choice of language, and of exemplars, emphasizes the fact that death is not something which happens only to those of us who will be unremarked except by birds and the bees—it is something which will demand surrender from everybody, even those who are far more important than those in the "alabaster chambers." Lords, princes, and other wearers of diadems will eventually succumb to death and will then simply lie in their chambers while the world continues above them, knowing that they are there, but moving on without them.