They've faced each other four times (advantage Brees, 3-1). They've won six Super Bowl rings (advantage Brady, 5-1). They've caught up with each other during multiple joint practice sessions, preseason games and Pro Bowls.
Yet when asked for some of his most lasting impressions of Brady over the past two decades, Brees still went back to their first meeting. In college.
"I'm gonna go way back," said Brees, whose New Orleans Saints will host Brady's New England Patriots on Sunday in the first-ever matchup of two quarterbacks with at least 400 career touchdown passes and the first meeting between two quarterbacks with at least 10 Pro Bowl selections, according to Elias Sports Bureau research.
"We played against each other in college in 1999, at Michigan," said Brees, who played at Purdue and remains the all-time passing yardage and touchdown leader in Big Ten history. "And that was at a point where the coaching staff there was having [Brady] share time with Drew Henson. Drew Henson was the highly touted freshman who I think had already been drafted in the first round by the Yankees. ...
"For me, standing on the sideline across from him, to me it was obviously Brady's team. And yet he had to share time with this freshman. And yet, man, his approach and his discipline during that time ... he played at such a high level, but he just worried about what he controlled.
"But I think that that probably shaped and molded a lot about him. A little bit of a chip on his shoulder, which has obviously served him well. And just a mental discipline and a mental toughness that's unmatched."
Brady's Wolverines trounced Brees' Boilermakers 38-12 on a rainy afternoon that was also a slopfest for Purdue's offense. There were so many dropped passes that Purdue coach Joe Tiller cracked, "I'd sue for lack of support."
Brees got his revenge years later, when he threw for a perfect passer rating of 158.3 in New Orleans' rout of the Patriots in their last meeting inside the Superdome in 2009, en route to a 13-0 start and a Super Bowl win.
Brady then returned the favor in 2013, with a game-winning TD pass in the final five seconds in New England that spoiled New Orleans' 5-0 start.
But Brady still couldn't help but rib Brees about the college meeting last year when they practiced together in similar rainy conditions in New England.
"We played 'em, maybe my senior year in the Big House, and we beat 'em," Brady said again proudly this week when asked about their long history together. "He was really in a fun offense to watch. Joe Tiller was a great [coach]. My roommate [when I first got to the Patriots] actually played with Drew -- Dave Nugent -- and he had so many great things to say about him. And I just loved watching Drew play even back then. And what he's done in the NFL and how prolific he's been and how incredible their offenses have been, it's really incredible.
"I have so much respect for him and everything he's accomplished, everything that he brings to the table at the quarterback position."
"If I can use 'we' in the sense of me and him, I'd say we probably both have the mindset that we want to change the norm for what is possible in regards to how long a guy can play and the level that they can play at." Drew Brees
Saints coach Sean Payton was the New York Giants' offensive coordinator when both Brady and Brees came out of the college, and he admits he missed the mark (along with all 31 other teams). Brady was drafted 199th overall in 2000, and Brees was drafted 32nd overall in 2001.
"I remember the evaluation of both players very well. ... And look, if any one of us had a crystal ball, you'd be taking them in the first three picks of any draft," said Payton, who was asked what he thought of Brady before he infamously fell to the sixth round. "He was tough. Lloyd Carr, who was coach [at Michigan], if I recall, told me he's the toughest player he ever coached. So you saw a little of that grit and toughness. He was a good leader. He had a strong arm. Those were some of the things.
"Listen, [former Giants general manager] Ernie Accorsi would have my evaluation. It's in New York somewhere."
When asked what he admires about the 38-year-old Brees as a fellow quarterback who probably appreciates the subtle tricks of the trade more than most, the 40-year-old Brady said, "Well, everything."
"I mean, he has ultimate control of the game," Brady said. "He's so savvy. I think he uses all the tools that he has at his disposal. He does a great job with the snap count, formations, motions, play-action. They do a great job of moving the pocket and moving him around. He can make all the throws. He knows how to look guys off. He knows how to throw guys open. He's got everything it takes. I think that's why he's thrown for 5,000 yards five times.
"That offense has been one of the top offenses in the league since he got there. He pulls the trigger, and his teammates have got a lot of confidence in him, and when they get it going, they're tough to slow down. They've got a great rhythm to their offense, and especially at home."
Brees will never catch Brady when it comes to championships.
And Brady will probably never catch Brees on the all-time passing yardage or TD lists.
Brees is already ahead of Brady on both lists, despite being 19 months younger. Brees (66,402 yards and 466 TD passes) is 5,538 yards and 73 touchdowns behind Peyton Manning for first place all time. Brett Favre ranks second in both categories. Brees ranks third in both categories. And Brady (61,849 yards, 456 TDs) is fourth in both categories.
Brady and Brees have one other thing in common. They both seem determined to keep playing well into their 40s -- and possibly break the NFL record for the oldest starting quarterback at age 45.
Steve DeBerg, Vinny Testaverde and Warren Moon all started games at age 44.
"If I can use 'we' in the sense of me and him, I'd say we probably both have the mindset that we want to change the norm for what is possible in regards to how long a guy can play and the level that they can play at," Brees said. "Listen, there's a lot that goes into that. You gotta take great care of yourself. You have to have some good things happen around you in order for that to happen. But I know for me, and I'm sure he can tell you the same for himself, you build a team around you of people that continue to help you be in the best position to succeed in regards to what you do for your diet and your rest habits and your recovery, your training and everything else. ...
"It doesn't look like he's stopping anytime soon. I don't know if there is a guy more diligent or disciplined in his regards to his recovery and his preparation and his mindset. One of the greatest of all time, if not the greatest. Certainly the championships will tell you the greatest. I've got a ton of respect for him. I've been playing against him since college and have a lot of respect and admiration for him."
When Brady was asked if he figures that no matter how long he plays, Brees will just play one day longer, he said, "It's possible."
"I mean, I know how much he loves the game and how committed he is," Brady said. "So, I mean, if anybody can do it, he can."
ESPN Patriots reporter Mike Reiss contributed to this report.