I disagree with your assessment. I will argue that only 2004 the Pats were a complete team. In 2001, the defense was great and the offense just really wasn't asked to lose. In 2003, the Pats had one of the most underrated defenses in league history and the offense was mediocre.
In all of the Pats' Super Bowls, you can point to one or two plays (or at least no more than a handful) which could have made the difference in the Pats winning and losing. In 2001, 2003, and 2004 the Pats were on the right side of those plays and 2007 and last year they were on the wrong side. Are you going to argue that it was because of the winning teams were complete and the losing teams weren't?
Sorry, but I would say that the 2003 team and the 2007 team were mirror opposites of each other. One had an amazing defense and middle of the pack offense and the other had an amazing offense and a middle of the pack defense.