@katylina,
I'm not sure what, exactly, your teacher is looking for but I see very little that the two works have in common beyond the use of the gimmick of the crew of a ship being shipwrecked on a remote island. In the case of Bacon, the island is located in the Pacific,off the coast of South America; in Shakespeare the location of the island is unspecified but some scholars, at least, have linked it to Bermuda in the Atlantic Ocean.
The Bacon work is what later came to be known as a 'utopian novel,' i.e. a work of fiction the purpose of which is to postulate an ideal world and what that world would need in order to be "ideal." In ]i]The New Atlantis[/i], this ideal condition is based on learning and research leading to new knowledge.
The Tempest, on the other hand, is a stage play, a comedy by Shakespeare, based on several disparate sources, but with hardly any 'moral' attached to it. In it Prospero, the Duke of Milan, plots to make sure that his daughter Miranda gets to succeed him as rightful ruler. There are political intrigues, there is some magic, and all it'sdone in fun with little or no preaching.
I don't know if this helps you any, but, again, not knowing what specifically you are looking for, it's hard to give a more comprehensive answer.