Intersecting themes in the two works deal with the rights of women in Victorian society, male domination in society and how they set the rules and expectations for women.
Aurora Leigh is a champion who redefines a woman's existence by deciding to stay unmarried and devote herself to her writing believing that to be a great poet she must surrender herself totally to the work, she shuns the idea of romance in favor of the solitude required by an author.
The Lady of Shallot by Tennyson can be viewed as a symbolic representation of how few choices Victorian women had and many which imprisoned them, like a loveless marriage or a controlling father who dismisses all suitors as unworthy, which results in the young woman being held captive in the family home without ever experiencing love or romance, and who escapes one day to find love or run away with a man rejected by her father, some she has fallen in love with. She leaves the protective environment, the family home, and figuratively dies to her family.
Elizabeth Barett Browning did not shy away from writing about hot button issues of her time.
"More than any other major Victorian poet, she explicitly and directly confronts political issues, particularly those concerning women. Like Tennyson, her husband, and many other contemporaries, she began as a disciple of Shelley who found the Romantic visionary mode compelling, and like them, she later developed a poetry of social, moral, and political commitment."
Using the two works, you could focus on the theme of how society imposes prisons on its members, particularly in this period in history, women.
"Elizabeth Barrett Browning's, Aurora Leigh (1857) argues that society imposes prisons on its members and that overcoming these prisons requires a strong will, much knowledge, and appreciation of true love and partnership. Aurora serves as Barrett Browning's example of the woman confined by society's unjust rules."
Tennyson examines a similar theme in "The Lady of Shallot." The lady imprisoned in the tower is a symbolic representation of young Victorian women who are held captive in their family homes as a way of protecting their virtue, honor and the family's reputation. The young woman is controlled, protected and guarded so that she can be matched in marriage to a suitable husband, found by her father or male relative.
Elizabeth Barrett Browning, before she married Robert Browning was literally kept as a prisoner by her father who was a tyrant.
"Elizabeth and Robert, who was six years her junior, exchanged 574 letters over the next twenty months. Immortalized in 1930 in the play The Barretts of Wimpole Street, by Rudolf Besier (1878-1942), their romance was bitterly opposed by her father,"
Or, the lady in the tower could be trapped by a marriage that was arranged by her father to a man that she does not love and who married her just to bear his children. She longs for real love, to be "in love," in the same way that Elizabeth Barret Browning describes in "Aurora Leigh" with regard to her main characters desire to be freed from the prison of that she initially puts herself in to become a great poet, life without real love.
"These lines show that Aurora has made a 360 degree turn since the beginning of her poem, when she spurned Romney's proposal. Now she believes that she must not live without the love she once cursed. "