More despair than hope, in my opinion. Although the hope encapsulated in the song of the thrush is clearly important, I think that it is all but drowned out by the patent despair in the surroundings and the description we are given of them. Hardy paints a bleak and desolate picture in the first two stanzas of a speaker that is divorced from the "household fires" of his fellow man and is put in the middle of a "spectre-gray" landscape that mirrors the death of the passing century as the wind sounds "his death-lament." One of the most effective pieces of imagery is the way that the "tangled bine-stems" are described as being "Like strings of broken lyres," which greatly adds to the picture of a broken chaos where there is no more place for celebration of music.
Into this picture of unyielding depression enters the thrush with his song of "joy unlimited," which seems to offer us the only hope that the poem contains as the speaker faces a new century full of despair. And yet this hope is massively undercut, for the vehicle of this hope is "frail, gaunt, and small" and is clearly himself oppressed by the natural elements, as he has a "blast-beruffled plume." Even his act of singing his song is described as something like a kamikaze act:
Had chosen thus to fling his soul
Upon the growing gloom.
How can such an act of "flinging" one's soul be anything but suicidal given the overwhelming bleakness of the setting and the "growing gloom" that is mentioned? The speaker himself is certainly confused by the bird's ability to sing a hopeful song when there is so little evidence of hope in their surroundings. Thus I would argue that while hope is present in this poem, it is almost swallowed up by the far more powerful force of despair.