I think some have assumed that because Dick LeBeau and Wade Philips are 3-4 coaches and they run tricky schemes, that Parcells necessarily would, too. But I think they are going to be disappointed. Parcells has always wanted to make football as simple as possible. He's a disciple of Lombardi, remeber. And you can see it in things like Parcells' emphasis on offseason conditioning and his comment that the most overrated thing in football is playcalling while the most underrated is execution.
But the simpler things are, the less likely you are to beat yourself. The more complex things you run, the more likely you are to have a miscommunication, leave something wide open, and give up big plays. Remember the Giants game last year where someone missed a call from the sidelines and Shockey made that big play on us? That's less likely to happen when things are simple and straightforward.
That's why I think everyone blaming Zimmer for things like Ware not moving around a lot last year are wrong. Parcells' vaunted Giants defenses, at least as I remember, were always very simple: An odd front defense and lots of cover-2 zone. Yes, LT moved around some, but that was more because he was such an incredible player that Pacells made an exception for him and let him freelance a little. But for the most part, that defense won because it had physically superior players that executed well.
That's not to say that Parcells won't let a coordinator who has earned his trust call different things, like he did with Belicheck. But that isn't his personal preference. He'd rather beat you up with bigger, stronger, better conditioned players than outsmart you.