Dimitroff did run things a lot differently in Atlanta than things were run here, but I do not want old guys back.
What the Patriots need is someone who understands where the league is heading and can acquire talent to fit that. In that, they need a cap guy who knows how to play the cap games that teams play now to make the cap virtually irrelevant. I will say that Matt Groh seems to buy into this concept and has said as much, but there is no way he would be allowed to do things like a lot of contracts with voidable years to spread out the cap (to my recollection, the Pats have only done that with Brady and McCourty).
The next GM also needs how to identify talent with speed and not one or the other. The Pats have acquired a few players with speed over the last few years, but few of them can actually play.
Also, the next GM needs to realize talent rules the NFL now more than ever. Back in the early 2000s, you could build a championship roster with a lot of solid yet unspectacular guys who worked together as a team putting team goals over personal goals. Those days are going away. The NFL is becoming more and more like the NBA where high end talent is what wins more often than not.