But the rivalry is heating up in late April.
First, Jets coach Rex Ryan wrote in his book that the Jets are the better team and the "big brother."
Giants defensive end Justin Tuck then responded by pointing to his Giants Super Bowl ring.
And now Pat Hanlon, Giants vice president of communications, is having some fun and responding to Ryan via Twitter.
In response to Ryan's assertion in his book "Play Like You Mean It" that the Jets would have beaten the Green Bay Packers if they met in the Super Bowl, Hanlon tweeted, "You gotta be in it to win it" and repeated a Giants motto: "Talk is cheap."
Hanlon also tweeted "Tom Coughlin wrote a book, too. It was about a team and an HC that won a Super Bowl."
The Jets organization released a statement Sunday night saying, "We'll let Pat enjoy his 15 minutes."
Hanlon responded to the Jets' statement, saying, "My 15 minutes has lasted almost 20 years. I happen to work for the best owners and greatest organization in professional sports. I hope they all feel the same way after 20 years. I know the Jets invented social media, particularly Twitter. We're just trying to perfect it."
Hanlon had re-tweeted comments by Giants fans talking about Ryan but later tweeted that Ryan "can coach his [rear] off" and that the tweets were in fun.
"If you're going to write about this, please mention the book," Hanlon said via email on Sunday. "Who knows, there may be considerations and then I won't consider this a complete waste of my time."
In a meeting that was arranged beforehand, Ryan will meet with Jets beat writers on Monday to discuss his book. He may be asked about what Tuck said last week in response to Ryan's boasts about the Jets being the better team.
"I'm gonna say this and this is gonna be the last time I comment on anything Rex Ryan says," Tuck told the New York Post. "The last time I checked, I have a Super Bowl ring and he doesn't, so if he's proud of coming up short, I guess he should be proud of that."
Ryan, who did win a Super Bowl ring as an assistant with the Baltimore Ravens, wrote in his book, "I know it's going to [tick] off Giants fans, but ... we are the better team. We are the big brother."
He added that the Jets are "going to remain the better team for the next 10 years. Whether you like it or not, those are the facts and that's what's going to happen."
The Jets and Giants are scheduled to meet on Dec. 24 in what will be a home game for the Jets.