What similarities exist between Shelley's Mont Blanc and Byron’s Manfred? Are there also differences worth mentioning?

Shelley's poem is a meditation upon the vastness of nature and the unknown it represents. Though Byron's Manfred is also set in the Alps, his theme is somewhat different from Shelley's in "Mont Blanc," despite points of contact between the ideas expressed by the two poets.
Byron's Manfred, like Goethe's Faust, is a man in search of the unattainable. Unlike Faust (in both Goethe's and Marlowe's versions), Manfred does not make a pact with the devil, Mephistopheles. Also, unlike Faust, Manfred does not appear to crave some "ultimate" experience that will give life the enjoyment he has lacked so far. Marlowe's Faust wants earthly rewards such as power and women. Goethe's character wishes for one thing that will make him say to "the moment," "Linger, you are so beautiful." Manfred, however, seeks "forgetfulness." His past is a torment to him, and he wishes to be relieved of it, to reach a state of oblivion. The "spirit world" he encounters, the Christianity to which the Abbot wishes him to return, and finally, the demonic figure at the close of the play are all rejected by him. His fate is an open question: the Abbot observes, at the final moment, that no one can know what has become of Manfred's soul upon his death.
Why does Byron set his "closet drama" in the Alps? Probably because the wilds of Central Europe were a meme of that time representing the mysterious, the unattainable, and the things which we all both desire and fear. In "Mont Blanc," Shelley similarly contemplates this highest peak of Europe and the surrounding immensity of forlorn nature—not so much wishing to merge himself with it and find oblivion as Byron does in Manfred, but as a means to understand himself and, by extension, to understand human thought, in the contemplation of the great mountain and of the "everlasting universe of things," as he describes it in the opening line. Much of the poem is, like Shelley's work as a whole, an indulgence in words for the sake of their own beauty:
Its subject mountains their unearthly formsPile around it, ice and rock; broad vales betweenOf frozen floods, unfathomable deeps,Blue as the overhanging heaven, that spreadAnd wind among the accumulated steeps.
It is really only at the close that Shelley reveals his ultimate theme: that the connection between man and this projection of the spirit world in the awesomeness of nature is what gives life its meaning:
The secret Strength of thingsWhich governs thought, and to the infinite domeOf Heaven is as a law, inhabits thee!And what were thou, and earth, and stars, and sea,If to the human mind's imaginingsSilence and solitude were vacancy?
Manfred, by contrast, though he communes with nature, finds no answer in it, no solution to the dreadful mental world he inhabits. In these two works, Manfred and "Mont Blanc," we see the Romantic obsession with the outside world, with nature, which paradoxically represents an inner world of the spirit that man wishes to attain. In both works, as well as in Byron's oeuvre and in Shelley's as a whole, there is a sense of man's incompleteness, of his striving for some unreachable goal that "this life" does not afford, though the manner in which each poem's speaker or protagonist seems to chase that goal is special to himself and unique.