This is something I've been thinking about myself recently. You still see Manning's mid-00s contemporaries like Brady, Brees, Roethlisberger and Rivers still playing into their 40s and still doing pretty darn well. At his peak, Manning had a credible case to be better than any of them, and his game would no doubt have aged well.
The biggest change is that Manning would stay on the Colts for at least a while, and the 2010-ish Colts were a garbage team with years of bad drafting behind them. Manning was dragging the team to playoff games almost single-handedly, but while he could carry them against bad teams, he couldn't carry them against playoff teams that fellow HOF quarterbacks and good rosters or coaches around them.
When PFM went to the Broncos, Elway went all-in to build a quality team around him ASAP before his neck failed. With a healthy Manning, I don't think Polian would have the same sense of urgency.
At the same time, Manning would be hard-pressed to leave the Colts, because the team gave him so much control on the field. I've heard from Colts fans that by about 2009, Peyton Manning was just straight-up running the offensive practices by himself, with little/no input from coaches. For a control freak like Manning, that has to be heaven. I don't know how much if any say he had in personnel, and maybe he leaves the Colts or ousts Polian after one failed draft too many. But if he left for free agency on his own, it would be a LeBron Decision-type drama bomb, and I don't think Manning was the kind of guy who'd want that much negative attention. He would exhaust all avenues with the Colts first.
Manning was at the peak of his game when his neck started failing him - MVP and what could have easily been a 16-0 regular season in 2009, MVP runner up in 2012, MVP and shattered every passing record in the books in 2013. So if he stayed with the Colts for another 6 healthy seasons after 2011 (calling it quits at age 41 sounds about right), I'll guarantee he gets at least one more MVP, probably two, three's not out of the question. He'd be in the running every single year.
But would he get to those two Super Bowls he got to in Denver? If his Colts teams are worse than his Broncos team, I'd say he either makes 0 or 1; flip a coin as to whether he wins it. If the Colts suddenly improve their drafting, or go full win-now mode and buy him a loaded team in free agency, he'll be showing up in the AFC title game perennially. Let's say he goes to 5 AFCCGs, he can turn that into two SB appearances without needing any kind of luck, and turn it into 1 win just on a coin flip. So that'd be a push with Denver. The opportunity is there for more if he gets a break or two, or less if he botches it and/or the Colts don't improve. So we can split the difference at 2.
For fun, let's say that Brady's arm starts fading after 2013, he's never the same guy again, Pats don't win another championship. Let's say that Manning's team improves after 2011, he goes to 2 more Super Bowls and wins 1. I know the OP wants a bit more detail than that, but this answer is focused on Peyton, lol.
The biggest change is that without having Brady to compare him to (or a Brady cut short), I think Manning is seen as hands-down the greatest quarterback of his era, instead of now where he's almost seen as an also-ran to Brady. If he finished his career with 2x Super Bowl wins, and Brady retires as *only* a 3x Super Bowl champion instead of a 6x Super Bowl champion (with the most recent of those Super Bowls coming in 2005), I think the "choker" label becomes much harder to apply in comparison. He'd be considered a "winner" and also run circles around the league in terms of individual stats and MVPs, so I think he goes down as the GOAT if his and Brady's situations are inverted.
