So you weren't following the Patriots back then. It's either that, or you were too young to remember. I'll take either explanation.
The '03 defense was and is still looked at as one of the top three defenses of all time. The '04 defense was still dominant, even with the massive injuries to the secondary.
By who, exactly?
Sorry, I can't let that one go by without responding.
The '03 Pats defense was a great defense. You can easily put them in the top 10 for the decade and make an argument for them being in the top 5. But, they don't even sniff the top 3 all-time.
'00 Ravens, '00 Titans, '01 Steelers, '02 Bucs, '03 Patriots, '04 Steelers, '05 Bears, '06 Ravens, '08 Steelers, '09 Jets. Those were the best defenses of the past decade, with the '00 Ravens and '02 Bucs in the conversation for best defense of all time. The '08 Steelers are in the conversation for top 10 all time.
The best defenses of all-time? There's no conclusive answer, but the '69-71 Vikings, the '76 Steelers, and the '85, '86, and '88 Bears all have to be included in any conversation. All of them were a notch (or several notches) above the '03 Pats.
They were a truly great defense, something we're not guaranteed to see in any given year, but to say that they were even close to being one of the 3 best defenses of all time shows an ignorance of NFL history.
As for the thread topic. Belichick is already in the Pantheon of great NFL coaches. Ryan has been a head coach for less than two years, he's off to a nice start, but that's it. If you want to isolate the defensive side of the ball, Belichick gets a slight advantage based on longevity, but Ryan is off to a fantastic start (Total Defense rankings since becoming DC in Baltimore: 5th, 1st, 6th, 2nd, 1st, 3rd. The '07 Ravens were 6th in total defense, but 22nd in PA due to 40 turnovers by the offense; the 14 INT and 26 fumbles lost led to Billick's firing).
There's a lot more that goes into being a great head coach than just being a great offensive or defensive mind. Norv Turner is a great offensive mind, that doesn't make him a great coach. That's where I think a lot of people may have misread the question. It's not asking who's a better coach, there's no need to ask that question. You won't find a better defensive mind than Rex Ryan. Whether he's able to grow into a great head coach is another matter altogether.