I think the Cahill comparison, from what I've seen, is not quite right. Cahill was very much played by Moyes as a very attacking midfield, almost an auxiliary striker. You'd often watch Cahill be very much uninvolved in matches, and then pop up with a goal. He wasn't a player who got his foot on the ball and dictated play.
Klaasen (or, as Koeman will surely call him, "Dayfee"), looks like a player who gets much more involved in the game. Dropping deeper, passing more, setting the tempo. Still with that ability to burst forward and make a vital contribution to an attack and pop up with a goal. Dare I say it, a more accurate comparison might be with Gary Speed?