While the Wanderer in the elegiac poem from the Anglo-Saxon period spends most of his elegy lamenting the loss of his homeland, family, king, and fellow seafarers, the speaker in Auden's Wanderer laments something very different.
Auden's wanderer seems to want to impose a self-exile based upon the fact that he finds the world around him too restrictive. Whereas the anonymous Wanderer seeks new friends and a new "Gold-friend" (a kenning for a king), Auden's wanderer wishes to rekindle the love between himself and the previously restraining woman in his life.
The Wanderer, in the end, finds hope in faith; for faith is the only thing that is able to survive in the world-men and kings will die. Auden's wanderer's search is, instead, for love. For it is love which he misses the most as he travels the "undried sea."
In the end, Auden's wanderer recognizes the power of love and wishes to return home to his, hopefully, faithful wife.
Ultimately, the main difference between the Anglo Wanderer and Auden's wanderer is that Auden's can see hope "with day approaching, with leaning dawn." For Auden's wanderer, he sees hope on the horizon; the Anglo Wanderer cannot.