Aaron Rodgers was lucky when he fell to the 24th pick in his draft, just not as lucky as Tom Brady was when he fell to the 199th in his. In 2005, Rodgers was picked by an iconic franchise with a history of fielding special players at his position.

Five years earlier, Brady was picked by a coach whose system helped land the quarterback in the Super Bowl in half of his 16 healthy seasons as a starter.

"I'm really a product of what I've been around, who I was coached by, what I played against, in the era I played in," Brady told ESPN.com last year. "I really believe if a lot of people were in my shoes, they could accomplish the same kinds of things."

What if Rodgers had been in those shoes for his entire career, playing for Bill Belichick in a New England Patriots system that rarely produces players who make the mistakes Green Bay's Ty Montgomery made Sunday, when he cost Rodgers a chance to beat the unbeaten Rams -- and ultimately got himself traded to Baltimore -- by turning the preferred touchback into a kick return and then fumbling the ball?

Rodgers, the 34-year-old one-time champ, is more physically gifted than Brady, the 41-year-old five-time champ, and nobody in Tom Terrific's household would bother debating that. In a conversation with an NFL coach within the past few seasons, Brady said that if Rodgers had the Patriots' offensive system and exhaustive knowledge of opposing defenses, "He'd throw for 7,000 yards every year. He's so much more talented than me."

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As such, it's no surprise that Sunday night's duel in Foxborough, Massachusetts -- hyped in an NBC promo by the GOAT of GOATS, Michael Jordan -- has been billed by some as a rare meeting between The Most Talented Quarterback Ever and The Greatest Quarterback Ever. Yes, there is a difference.

Accomplishment > Talent. And Tom Brady is the most accomplished football player of all time.

But with Belichick, Brady has enjoyed the benefit of playing for arguably the greatest coach of all time. On the other side, Rodgers has been paired with Mike McCarthy, a good coach and a Super Bowl winner who deserves his fair share of credit for developing Rodgers the way Vince Lombardi and Mike Holmgren deserved theirs for developing Bart Starr and Brett Favre, respectively. If McCarthy is a widely respected character actor in this drama, a Brian Dennehy or Paul Giamatti, Belichick is a Marlon Brando or Robert De Niro.

Would Rodgers own multiple Super Bowl rings if he'd starred alongside Belichick?

Up front, understand that Belichick has never had a franchise player with Rodgers' skill set. Of his four main quarterbacks in Cleveland and New England -- Bernie Kosar, Vinny Testaverde, Drew Bledsoe and Brady -- only Testaverde would qualify as athletic, and he rushed for more than 200 yards in a season just once. Rodgers has eight seasons of 200-plus rushing yards, including four of 300-plus, while Brady has never run for more than 110 and didn't crack 50 in seven seasons.

Rodgers also happens to be the only man in NFL history with a passer rating north of 100. (He's at 103.6; Brady is third on the career list at 97.6.) Although Belichick is on record saying, "There's no quarterback I'd rather have than Tom Brady," he could conceivably scheme things with Rodgers' balletic feet that he can't scheme with his own No. 12. Brady, for instance, does not have in his golf bag that escape to the left and impossible, against-the-grain sideline throw Rodgers made to beat Dallas in the playoffs two seasons ago.

How Tom Brady, Aaron Rodgers Compare in Rate Stats Brady's career stats dwarf Rodgers', but the Packers QB compares favorably in several rate stats. Category Tom Brady All-Time

Rank Aaron Rodgers All-Time

Rank Passer rating 97.6 3 103.6 1 QBR* 74.2% 2 70.1% 6 INT % 1.8% T-2 1.5% 1 TD % 5.5% T-23 6.3% T-6 Cmp % 64.0% 13 64.9% 8 Y/A 7.5 T-26 7.9 T-5 ANY/A 7.12 3 7.42 1 *QBR data goes back to 2006

"The system would be different with Rodgers," said one former Belichick assistant who has competed against Rodgers and Brady. "Those lateral underneath passes to those small receivers, that fits Brady better. Rodgers is such a good athlete with such a big arm, I think Bill would use more vertical stuff down the field and move the pocket more than he does with Brady."

Beyond calling for additional rollouts and bootlegs, Belichick, a details freak, would undoubtedly maximize Rodgers' mastery of the free play -- his ability to punish pass-rushers he has drawn offside with a hard count and punish a 12th defender who is late getting off the field by barking out a code word signaling an immediate snap.

"But the athleticism is the difference," the former Belichick assistant said. "That's not saying it would translate into more championships because how many more could you win than Tom's won? Rodgers and John Elway are the two most physically gifted quarterbacks ever, but the only thing Rodgers has that Brady doesn't is that ability to move around. Brady has a natural instinct for manipulating the pocket, for knowing when to slide laterally within the pocket, and mentally Tom and Joe Montana are as good as there's ever been as far as their pre-snap ability to look at a defense and know exactly where to go with the ball."

Bill Belichick is 27-10 in the playoffs as Patriots coach, with five Super Bowl championships. Aaron Rodgers has one Super Bowl title in Green Bay. Matthew J. Lee/The Boston Globe via Getty Images

Brady has won far more regular-season games (202) and postseason games (27) than any quarterback dead or alive, and his unmatched competitive drive is chiefly responsible for his unmatched record. How much Brady has elevated Belichick's system and how much Belichick's system has elevated Brady is a sports-bar argument that can't be settled conclusively. "But that Patriots system did go 11-5 with Matt Cassel when Brady was out in 2008," one league executive said of the quarterback with the 36-45 overall record. "And I think Green Bay is 3-13 without Aaron Rodgers."

Meanwhile, a second league executive questioned how Rodgers would coexist with Belichick and his unforgiving style of coaching. Until their relationship finally and temporarily unraveled last season, their 18th together, Brady and Belichick had maintained a near-perfect transactional partnership. Belichick treated his best player as if he needed to earn his scholarship every day in practice and in the film room, and Brady -- hardened by five tough-love years under Lloyd Carr at Michigan -- responded as if he would have it no other way. Rodgers is known to be a sensitive sort with an ego healthier than his left leg. Would he have matched Brady's willingness to manage Belichick's Belichick-ness while accepting below-market contracts for the benefit of the overlord's greater good?

Rodgers has spent precious little time around the Patriots coach. Unlike Peyton Manning, he has never played for Belichick in the Pro Bowl. Rodgers merely mopped up for Favre in a blowout loss to New England in 2006, and he missed the scheduled 2010 meeting between the two teams while suffering from the lingering effects of a concussion. In their one and only head-to-head matchup, Rodgers defeated Belichick/Brady 26-21 at Lambeau Field in 2014. Brady won his fourth Super Bowl ring more than two months later -- two weeks after Rodgers' bid for No. 2 was foiled by Seattle.

That year, when asked about the similarities between his guy and Rodgers, Belichick deadpanned, "They both wear No. 12." The truth is the quarterbacks have plenty more in common than that. They grew up 3½ hours apart in California and used real and imagined slights to fuel their inner fire to be great. Brady was once a backup quarterback on a winless high school freshman team and a seventh-stringer at Michigan who went through hell to get on the field. Rodgers used his rejection letter from Purdue as a constant reminder of those who found him unworthy of a full Big Ten ride.

"Mr. Chicken Legs," one Butte College staffer called the junior college quarterback with the spindly wheels and a work ethic that drove him from Butte to the University of California, Berkeley to Lambeau Field, where fans initially wanted no part of Favre's replacement.

"If you go by championships to determine the best quarterback, you have to go with Brady. But if you go by who's the most complete quarterback, you have to go with Aaron Rodgers." Michael Bishop, former Patriots quarterback

But what if fate had dropped Rodgers on the Gillette Stadium doorstep instead and placed him in a Belichick program that had passed on Brady in the 2000 draft?

"It would be limitless what Aaron would've done with Belichick and that organization," said former Butte head coach Craig Rigsbee, who recruited Rodgers to the community college and remains close to him. "The genius of Belichick is that he evolves all the time on offense and defense, and that's one reason why he's stayed on top for a long time. Belichick and [offensive coordinator] Josh McDaniels would've done some crazy stuff with Aaron because he has all the intangibles Brady has and better arm talent, and he's a much better athlete. I think Aaron would've won four or five championships, too."

The first NFL executive to make Belichick a head coach, Ernie Accorsi, isn't so sure about that. The retired general manager who hired Belichick in Cleveland in 1991 -- and who acquired a Hall of Fame quarterback, Elway, and a potential Hall of Famer, Eli Manning, on draft days 21 years apart -- said there are too many unpredictable variables to say whether Rodgers would've won more with Belichick than the one championship he has claimed with McCarthy.

"I've always believed that Montana had to have Bill Walsh, that Dan Marino had to have Don Shula and that Starr absolutely had to have Lombardi," Accorsi said. "I'm a big believer that quarterbacks need certain coaches, but I'm also a firm believer that Bill would've created a successful system in New England no matter what style of quarterback he had.

Tom Brady and Aaron Rodgers have faced off only once, with the Packers beating the Patriots 26-21 in November 2014. Christian Petersen/Getty Images

"I think Bill would have been different with Rodgers, with his mobility. He's too creative and too smart to not have adapted his style. But would Bill have won as much with Rodgers as he has with Brady? I don't know. Brady's the only guy I've ever watched play that position in my lifetime who makes it look easy. Brady's not a runner, but he's got great rhythm with his feet. The fact that Rodgers can escape is a bonus, but ... I don't know what would happen. When you move players around hypothetically in different situations, the stars are realigned. There are no analytics on those things."

Which is why it is so fun to imagine them, to try them on for size. One former player with a unique perspective on the fictional Belichick-Rodgers partnership is Michael Bishop, who was drafted by New England and signed by Green Bay in his brief NFL career (he played for years in the Arena and Canadian leagues) and stood ahead of Brady and behind Bledsoe on the Patriots' depth chart in 2000. Bishop and Brady used to hang out together, and one night they promised each other that if one took the job from Bledsoe, he wouldn't ever give it back. Brady honored that promise, but not until Bishop, the most mobile quarterback Belichick has ever coached, threw a Hail Mary touchdown pass against Indianapolis in 2000 and became a popular choice among some vocal Patriots fans to replace the lead-footed Bledsoe.

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"When I first came into the league, the way I played the game and the way I moved -- I don't think Bill Belichick was ready for that at that time," Bishop said Tuesday by phone. "The whole league then was based around guys like Bledsoe, 6-[foot]-4, 6-[foot]-5 guys who could sit back there and throw it all over the yard. I don't hold anything against New England or Bill, but they never had anything like me. The game has changed, and now you have quarterbacks like Aaron Rodgers who can get outside and throw on the run, and that is four quarters of stress you're putting on the defense.

"I think Bill today would definitely adapt to a mobile quarterback and find different ways to move the pocket and get outside. He won five championships with Brady, but if you put Rodgers in there, the sky's the limit for them. If you go by championships to determine the best quarterback, you have to go with Brady. But if you go by who's the most complete quarterback, you have to go with Aaron Rodgers."

Rodgers-Brady is very much a mutual admiration society. As a younger player, Rodgers studied Brady on film and admired his accuracy, his pocket presence and the way he took care of the ball and controlled a defensive backfield with his eyes.

Bill Belichick's 256 career wins rank third all time among coaches. He and Tom Brady are in their 19th season together. AP Photo/Chris Jackson

On his end, Brady has consistently said he loves watching Rodgers and that the Packers quarterback does things nobody else can do. "Aaron's one of the best to ever play," Brady said after beating Buffalo on Monday night. On his weekly radio appearance on Boston's WEEI on Tuesday, Brady called Rodgers "inspiring" and said the Green Bay quarterback "makes me want to get out there and practice and improve because I think he's so phenomenal with how he manages himself in the pocket. His ability to throw the football is unlike anyone in probably the history of the league. It's pretty awesome to watch. He throws some of the best incompletions I've ever seen."

And some of the best completions, too. So yes, Belichick and Rodgers would've made for a devastating fantasy football tandem. Forever worried about the threats opposing mobile quarterbacks pose, Belichick would've finally had one to call his own. "He's a great player," the Patriots coach said of Rodgers before their 2014 faceoff. "He does a tremendous job, really, at everything. He has no weak points. Makes every throw. ... He's a hard guy to tackle, a hard guy to get and a very good thrower, a very accurate thrower, and has great vision. He's really good."

He's also really lucky to have played his entire career in the instantly recognizable uniform of a fabled franchise. Just not as lucky as Tom Brady, who ended up with the coach and system that helped him become the greatest quarterback ever, if not the most talented.