Who here is talking about the great 2001 defense? It was far from great, but it was still way better than this one. Wasn't one of Belichick's first comments after they won the SB something to the effect of "I can't believe we won it with these guys?" That team, as constructed, shouldn't have been good enough to win the SB. That pretty much sums up why it remains my favorite Patriots team, to be honest. It had no business winning, but it was consistently the best-coached, most innovative, and luckiest team in the league.
While that makes it an awesome team to root for when it happens, it's also not a very good blueprint. I'm not sure that making this team more "2001-esque" is a good thing. More 2004-esque, sure, but that 2004 defense was filthy.