I agree with you that personnel has been a big-time issue for the defense over the last 3-4 years, but I think one-gap/two-gap is part of the issue as well.
Not only did the Patriots have elite personnel in those glory years of 03/04, but the league was a different league. The rules have changed since then. The league has become much more of a passing league than it was back then. Back then, guys like LaDanian Tomlinson and Larry Johnson were carrying the rock 350 times per year and approaching 20 TD's per year. That doesn't happen anymore. Not only are two back systems more prevalent, but the NFL is more pass-oriented now.
In 2009, there were 10 QB's who threw for over 4,000 yards. In 2003, there were 2 QB's who threw for over 4,000 yards. You look at the last few years, and QB's numbers are way up. Brees threw for over 5,000 yards in 2008. The QB's are getting better and better. Very few teams are built around a running game -- the NFL is trending much more towards a QB driven league. The Jets have had a great running game and a great defense for the past two years, but they've eventually fallen to teams with better passing attacks and QB's.
Rex took Mangini's 2008 middle of the pack Belichick-styled Jets defense and turned them into the most dominant defense in the league in 2009 with more or less the same personnel. Teams like the Packers, Saints, Steelers, and Giants have all won Super Bowls with similar philosophies on defense -- aggressive one-gap schemes. This style of defense just seems to be the better way to go about defending opponents with the way teams are chucking the ball around the field.
It's just a personal opinion of mine: I think the two-gap defense is a bit outdated for the pass-happy NFL. I'm not just getting caught up in the media frenzy of this training camp and the alleged evolution of the D, I've felt this way for quite a while now (go back and check some posts if you want to from 2009 on).
While I agree that personnel has been a problem for this team on defense, I believe scheme has too. It is hard/difficult to find DL for the 2-gap 3-4. Seymour-types don't grow on trees. McGinest and Vrabel-types don't grow on trees. A one-gap scheme is much easier to address needs with. You can go after some undersized edge rushers. You can go after some shorter/squatty DL who excel at shooting gaps. You can get a more immediate impact from a college player that you draft. I think a guy like Cunningham would be much more productive coming right out of college and being plugged in as a DE in a one-gap 4-3 scheme rather than trying to learn the techniques/coverages/intricacies of a 2-gap 3-4.
You've made this argument in the past. It was wrong then, and it's wrong now. There's no sense going deeply into it again, though, because the data and the results have shown you wrong, yet you refuse to just admit to the evidence. Therfore, I'll just point out that the scheme you're crying about is precisely what's enabled a talent deficient defense to remain at the top end of the defensive rankings over the past 3 years, despite the loss of most of the best players.
Bruschi
Harrison
Vrabel
Seymour
Warren
Those guys are gone, and the only one who's replacement has been anything like a fair swap has been the Bruschi/Mayo swap.
Warren for Warren.... no
Everyone for Seymour.... no
Ninkovich et al for Vrabel.... no
Sanders and/or Meriweather for Harrison.... no
The talent has clearly declined, yet the defense has managed to remain in the top ten in scoring. In fact, here's the defensive scoring ranking since the start of the Super Bowl era:
6
17
1
2
17
2
4
8
5
8
There is nothing there that shows any kind of league catching up against that defense. A team with Deltha O'Neal as a starting CB managed to finish in the top ten on defense. Last year's team managed to finish in the top ten on defense, despite having 2 holes on the defensive line, 2+ holes at linebacker, a hole at starting CB and a hole at the nickel CB.
One last note, since you were talking about the attack style teams. The only 3-4 team that can compare with the Patriots defensive dominance during the Patriots Super Bowl era is the Steelers, and even they've had more seasons outside the top 10 during that time (4-2). In fact, since the last time the Patriots finished outside the top 10 in defense, the Steelers have done it twice (2006 and 2009). The best 4-3 team during that time, the Ravens, have finished outside the top 10 three times, most recently in 2007.