The advantage in this scheme is that the public (and Gertrude) will not know that Hamlet's death is murder; since it will happen in the middle of a fencing match, it will look like an accident and neither Laertes nor Claudius will be blamed.
A disadvantage though, is that since Hamlet has escaped from all of Claudius' other plans he might escape from this one too, or it might backfire and end up harming more people than just Hamlet.
