The thrush and the poet are the only living things in this otherwise dead landscape. The poem emphasises for both their innermost being: for the bird it refers to his'soul' and for Hardy it refers to him as a 'spirit'.
They both respond to their environment: the former in song and the latter in poetry.However, they strongly contrast in the nature of their responses to this adverse environment. The bird chooses to 'fling his soul' upon it, the words suggesting an act of defiance. Hardy meanwhile, succumbs to its desolation, even adding his own where he fancies the landscape to be stretched out like ' The century's corpse'. He personally sees no cause for optimism in advancing modernity, and it affects the way he views this admittedly bleak vista.
The most telling contrast is this: the bird's song is an expression of 'blessed Hope' which the poet can appreciate but not share. He is 'unaware' of and not 'blessed' by the Faith which can produce such Hope.
To be honest, it is the differences between the thrush and the poet that is the point of this excellent poem. However, both the thrush and the speaker are presented as being alone in an otherwise desolate landscape. There are no other forms of life present except for the poet, leaning upon his "coppice gate" and the thrush singing joyfully in spite of the desolation around him. Likewise, the physical description of the thrush seems to match the spiritual or internal description of the speaker. Note how the thrush is described:
An aged thrush, frail, gaunt, and small,
In blast-beruffled plume...
The emphasis on the frail nature of the bird perhaps is echoed by the pessimism of the speaker in this poem, who, like the thrush, finds himself "gaunt" and "small" and "beruffled" when faced with the bleakness of the world and of the created order.
However, the essential difference is that the thrush is able to sing and find some evidence of hope in what he sees, whereas the speaker is not.