Elizabeth I is one of three female monarchs who have ruled longer than any male monarch in England's long history.
Elizabeth was bright, with a disposition like her father's. While the rest of Europe considered Elizabeth illegitimate and wondered if Henry was really her father, Henry always acknowledged Elizabeth as his child.
Upon his death, Elizabeth was imprisoned by her half-sister Mary. Elizabeth realized quickly that she needed her wits about her to avoid being embroiled in political intrigue. She was very good at this.
When Mary came to the throne, as a staunch supporter of Catholicism, she killed hundreds of Protestants, and earned the name of Bloody Mary. (England was happy when Mary died, mostly for this reason.)
Mary did not like Elizabeth (a Protestant), nor did she trust her, but she couldn't kill the princess (who had many followers), so she kept Elizabeth as a prisoner for several years. When Elizabeth was twenty-five, Mary died, and Elizabeth became Queen.
Elizabeth spent the remainder of her life ruling the English throne like her father. She was unmarried, but encouraged proposals from several countries, even Spain. (Mary had been married to Philip of Spain.) Because of years of fighting between the royal houses, the Tudors were almost bankrupt. So Elizabeth welcomed her suitors' expensive gifts for the treasury. Though Elizabeth did not encourage Francis Drake's attack of Spanish ships returning with treasure from the New World, she happily took it.
Elizabeth steered a more tolerant course between the Protestants and Catholics, and she was a formidable ruler. When Essex, a favorite, tried to take the throne, sad and disappointed, she had him killed. With proof that Mary, Queen of Scots supported Elizabeth's murder, the Queen had to executed her also. To bring peace and growth to England, Elizabeth welcomed the "rebirth" of the arts, called the English Renaissance. Elizabeth was a woman of courage and intelligence.
Lady Macbeth, in Shakespeare's Macbeth, is also a strong and intelligent woman. She is bold, as was Elizabeth, but she has no honor, and plans to be queen with the murder of her King. Macbeth says that she is so harsh, that she should only give birth to boys.
Bring forth men-children only,
For thy undaunted mettle should compose
Nothing but males. (I.vi.81-83)
Lady Macbeth even calls on the powers of darkness to take away anything "soft and womanly" about her so that she can do what must be done to murder the King.
… Come, you spirits
That tend on mortal thoughts, unsex me here
And fill me, from the crown to the toe, top-full
Of direst cruelty!… (I.v.41-44)
After Duncan's murder, Lady Macbeth comfort Macbeth, so he need not feel guilty:
My hands are of your color, but I shame
To wear a heart so white…
A little water clears us of this deed:
How easy is it then! (II.ii.80-86)
Both women are strong. They speak up and are wise in dealing with the path to power and success. However, Lady Macbeth is evil: achieving her ends with murder, while Elizabeth used intelligence and strategy to get things done. Elizabeth refused to lie to Mary in order to be released from imprisonment. Lady Macbeth smoothly lies to Duncan when he comes to Macbeth's castle, even while she plans his murder. Elizabeth I and Lady Macbeth may be strong women, but Elizabeth I had integrity. Lady Macbeth is not noble: she will take whatever shortcuts are needed for her own gain.