@sans_fi
I like the idea of Grievous grabbing Anakin's saber, but I don't think Anakin needs to grab Grievous's. Can't we just imply that he constructed a new saber between being indoctrinated and the Mustafar battle? It would also imply some passage of time of you move things around a bit so Anakin's turn won't seem as sharp or sudden.
Also, Grievous taking his sabers from dead Jedi makes him such a badass and in the 2D clone wars series (he's like a jedi slayer, a prototypical Darth Vader). but I agree that in the film it does nothing and I think he looks more menacing with red sabers.