These two sonnets are two of handful of Shakespeare's most famous sonnets. Both sonnets have a negative and bitter tone to them and suggest that the speaker is unhappy with some aspect of his life, and both sonnets emphatically state that love or friendship are the cure for such a state. Sonnet 29's opening octave is a laundry list of everything that is making him unhappy. He opens with the idea that he is "disgrace with fortune (fate) and men'seyes" so that means both heaven and earth causing him trouble. He is "outcast" and can't even be sure he prayers are being heard, assuming that he is praying to a "deaf heaven." He goes on to list the specific things that upset him --he is essentially jealous of things that everyone else has: hope, good looks, good friends, skills and abilities. He concludes the octave with the idea that he despises himself. Sonnet 73's chief complaint is the speaker's recognition of his growing old. Each of the quatrains uses a metaphor of aging: yellow leaves on nearly bare trees, the twilight of a day, and the low flames of a fire that is nearly extinguished in its own ashes.
Both poems conclude with a turn in the mood of the speaker that lightens the theme of each sonnet to say something positive about how love or connection to another person can change the perspective of the speaker. Sonnet 29 uses the entire sestet to convey that the mere thought of the beloved makes his "state (of mind) sing hymns at heaven's gate" when he remembers the "sweet love." He is brought to contentment and satisfaction. Sonnet 73's final couplet says that if the listener of the previous lines understands the inevitable aging of a person then the knowledge that the person will someday be gone should make the love grow stronger when that person is still here. To simplify, it is important to love while we have the opportunity.
The sonnet structure of each poem helps the reader see the argument that Shakespeare creates in each. Both poems end on apositive note that wasn't necessarily expected based on the the tone and content of the first lines of each sonnet.