In “Sonnet 71,” the speaker urges the beloved to forget about him quickly when he dies. He does not like the idea that remembering him could make his beloved sad someday. However, the speaker is still using the poem as a way to be remembered. In “Sonnet 75,” the speaker discusses writing his beloved’s name and seeing it washed away. One central idea in the poem is that writing might not last, but love will. This is different from the Shakespearean sonnet, where the speaker wants love to fade so that his beloved will not be sad.
Both discuss their love for another; Spenser says his love will outlast the world, while Shakespeare wants to be forgotten in order to spare his love any pain.
Spenser is trying to immortalize his love, although the waves (or the natural world) wash away his words. The tide says that Spenser is being foolish. However, at the end of the poem, the final couplet adds further meaning: that nothing lasts forever -- except for their love.
Shakespeare's poem is a bit more negative. He says that after his death, his love should not mourn him. Shakespeare says he so loves the subject of the poem that he would rather be forgotten than a source of grief. The couplet adds further meaning to this idea by saying that he doesn't want his love mocked for his grief.
Thus, both poems discuss love and the passage of time; their individual messages differ.