I cannot write your paper for you, of course, but I might be able to give you some direction to get started.
There was a great deal of dissension between Elizabeth I and Mary Queen of Scots. Elizabeth I was a masterful leader of the state, quite adept at holding her own against male leaders of the major powers of the time (i.e., Spain), as well seeming without equal in raising England out of its enormous debt after so many years of fighting between the royal houses in England. She was also a patroness of the arts, and England experienced a booming renaissance with regard to the literature, music, etc. She was able to be as harsh as her father, Henry VIII, when necessary, but was quietly be able to steer the nation toward peace, even religious peace (though there is talk that she was not as light-handed in this regard as some history books report). She was also Protestant, which former supporters of her deceased Catholic sister Mary, deplored.
Mary Queen of Scots did not have the power or the grace and charm of Elizabeth. Mary was a schemer who wanted England's throne. She married the heir to the French throne, but he died soon after. Mary returned home to a Protestant-dominated country that wanted no part of Mary's scheming. She married again, but Lord Darnley was jealous and murderous: he was found strangled in the ruins of a castle fire, but Mary did bear a son by him, James VI of Scotland. Three months later, Mary married again, much to the outrage of of the Scots, and because of the political threat she posed, Elizabeth had her imprisoned for eighteen years.
There were still dissenters who wanted Mary to be Queen of England. During the later years, letters addressed to her were discovered that suggested a plot to kill Elizabeth and put Mary on the throne. Elizabeth I was a true "renaissance woman," but still very much like her father. She could not allow such treason to continue, and so Elizabeth had Mary beheaded.
Ironically, and probably much to the Queen's chagrin, when Elizabeth I died—the longest ruling monarch on the throne up to that point, and a woman as well—she had no heirs as she had never married. Her only option was to name James VI of Scotland, who became James I of England.
So while Mary was never Queen of England, her son was to become the King of England. It was in this way that the Tudor line ended, and the Stuart line came to the British throne.
You will need to research more details, but this is an overview. Good luck.