A great example of the similarities these two epics share deal with relationships. In the epic saga of Starwars Obi-wan Kenobi previously knew Darth Vadar from training him to be a jedi. These two old friends end up believing differently about each other, and their thoughts, as Darth Vadar begins to give into the "dark side". The "dark side" is using the force to manipulate others in a harmful way. A similar relationship is shown in Beowulf as Hrothgar once sheltered Beowulf's father.
Another example of these similar instances from the two stories would be Beowulf and his 14 fine men. He brought them with him to help fight off Grendal the menacing beast that has been harassing Heorot for 12 years. Similarly, in Starwars Obi-wan has asked Luke Skywalker to aid him in the battle against the Empire and in a mission to rescue Princess Leia from the grasps of the Empires lead men and Darth Vadar.
If there are similarities there are going to be some differences. A great example of one of these is how Beowulf starts out with a brief history about the Royal Dynasty which was named after a mythic hero, Scyld Scefing. However in Starwars there is no history of a land or even a history at all at the beginning. However there is a history in the end when it shows the history of Luke Skywalker after he has saved the galaxy from Darth Vadar and disturbed the empires plans on eliminating the Rebels and Jedi's.
Another difference is when Beowulf goes with 11 of his men to the dragon's barrow and tells them that he is going to go in alone to fight it. Yet his Wiglaf goes to assist him in this battle with the beast. In Starwars Luke Skywalker is about to duel Darth Vadar to the death but doubts himself until Obi-wan sends him a "force"...