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.