How does the role of the Player as Shakespeare portrays him compare to Stoppard’s portrayal in Rosencrantz and Guildenstern Are Dead?

There is a significant different between the player in
Shakespeare's Hamlet and in Stoppard's Rosencrantz and
Guildenstern Are Dead.  In Shakespeare's play the character of the play has
absolutely NO personality.  He arrives, he performs a speech from a Greek play, he
agrees to change a few lines for Hamlet; he performs the "play within the play" and is
never heard from again. 

The Player in Stoppard's play is
arguably the most important character.  It is through him that Stoppard can make his
point about the lives of Rosencrantz and Guildenstern.  Ros and Guil seem pretty lost
and frustrated about their situation in this play -- they know they were called to find
out what is wrong with Hamlet, but they fail miserably and spend a good deal of the play
playing games and talking about seemingly random topics.  Ros wants to go home; Guil
tries harder to figure out what is exactly going on with their lives as well as
Hamlet's.  It is the Player though that brings all of this into sharp focus.  Ros and
Guil ask for guidance and the Player tells them "it is all written."  He tells them that
they are "nobody special."  He tells them they should be careful "not to lose their
heads."  He seems to know everything that is going to happen to them -- and he is
taunting them with the knowledge.  How can that be?  He is an actor in a role and he
knows it.  He lives on at the end of Shakespeare's play so he 'knows' how it will end. 
Ros and Guil die at the end of that play, so they don't remember anything.  It is an
interesting study in the reality of characters and authorial control of
characters.