Nothing captured the differing ways more than when ESPN's training camp tour bus visited the Jets and then the Patriots the following day. Jets coach Rex Ryan signed the bus with the words "soon to be champs;" Patriots receiver Wes Welker responded by writing "one game at a time."
The Jets go brash and happily fill opponents' bulletin boards, while the Patriots button their lips, verbally build up the opponent all week, then attempt to play the role of silent Sunday assassin.
"I knew the bus was going up there next, and I wasn't sure who would be [on it], but I knew they would certainly get a charge out of it," Ryan recalled of his antics. "And they did."
Now imagine Bill Belichick doing the same thing.
Just wouldn't happen.
"We just go about our business a different way," quarterback Tom Brady said. "Every coach has their style, and we really take on the style of our head coach, who doesn't say much. So we typically don't say much, and when we do, we get yelled at pretty good. It doesn't seem that's the program the Jets are on. That's the way it is."
Not that Brady is passing any judgments.
"Who knows what's right or wrong? Our styles work for us, and that's what is most important," he said. "We're not trying to be the Jets, and they're not trying to be the Patriots."
Brady sees similarities when it comes to style of play, as both teams take pride in being physical and tough. Both defenses also run the 3-4 alignment, albeit in different forms, but that's about where it ends.
"Everybody has got a different style, so I don't think there is anything wrong with that," Belichick said of his interactions with Ryan. "I have a lot of respect for Rex and what he's done. He's always been successful as a coach wherever he's been."
Ryan echoed similar words during a Wednesday afternoon conference call.
"Do we go about things differently? I think that's just the way Bill is. I think he's always true to himself. He knows what he wants from his team and all that," he said. "And I'm going to be true to myself, so I think we're a little different there, the way we approach things. But I think we're both after the same thing."
Belichick pointed out that while he doesn't know Ryan well, he goes way back with members of his family. When Belichick was Browns head coach, he held practices with Buddy Ryan's Cardinals teams. And Rob Ryan, Rex's twin brother, was a Patriots assistant from 2000 through 2003.
"My brother has two Super Bowl rings that obviously the entire family is proud of," Rex Ryan said. "He thought the world of Bill. He said you think you're pretty good when you're a move or two ahead of somebody, but he always said that Belichick was four or five moves ahead of that.
"I have always said that I think he's the best coach in the league, but again, I'm here to beat him," Ryan continued. "It's not about my skills against his skills; we'd lose that. It's about his team and my team, and I have confidence in my team and I know he's got confidence in his team, as well he should. But we get to see what happens on Sunday."
The differences between the Patriots and Jets extend beyond the coaches to their team-building approaches.
Consider that the Patriots made 24 selections over the past two drafts, while the Jets had just seven. Also, while the Patriots have generally shied away from big-name acquisitions, the Jets went heavy in that direction this year with the likes of Santonio Holmes, LaDainian Tomlinson, Antonio Cromartie and Jason Taylor.
So whether it's building through the draft or free agency, taking a long-term approach instead of focusing more on a short-term fix, or filling up a bulletin board versus buttering up an opponent, the Patriots and Jets are at opposite goal lines on the football field.
They do things differently, and seeing those styles clash throws another log on this fiery rivalry.
Mike Reiss covers the Patriots for ESPNBoston.com. Follow him on Twitter.