The two stories are similar, i.e. Hamlet kills his uncle, who has murdered his father, married his mother and taken the throne but few details after that are as Shakespeare made them. Amlethus took the throne, married and had a son. It is viewed as unlikely that Shakespeare read Saxo, probably on the basis of Jonson's comments that Shakespeare knew little Latin. I read a book called Shakespeare and Ovid, by Jonathan Bate, where he argued (and rather convincingly to me) that Shakespeare knew more Latin than he was given credit for. However, Shakespeare was not concerned with historical accuracy but art and satire in his plays.
Bliss' argument was for Eomer to be Hengest's real name, making his great-grandfather Hamlet's killer. Only thing is that, in Beowulf, there is a digression on Eomer as well as the Finnsburg Episode so why would the poet talk about them as separate persons if they were one and the same? I have ordered Saxo's book. It looks like a good read.