Brady has thrown the fewest picks, though it's debatable which way that cuts -- INTs are accounted for in QB rating, and advanced analysis suggests that INT rate regresses to the mean much more than YPA and completion percentage. And it's pretty clear that Manning has the worst receiver corps of the three. In sum, I don't see any way you build a statistical case for Brady over the other two, particularly Manning.
First, there's like maybe a 1% chance RG3 and Rodgers are even considered. Not happening. The narrative is Peyton and Brady, they have their history, have better teams, and the Brady v Manning makes for a more compelling storyline.
But, this int rate thing -- I don't buy it at all. There's a reason Brady is routinely around 2% int rate, and his career is the same, and it has nothing to do with adjusting anything to the mean / regression. He just makes better decisions. Brady's and Manning int % this year is right in line with what they typically do -- and this same argument can be said about their careers. Peyton will have some more volume stats, Brady is more efficient. This is the players in a nutshell.
As far as the worst receiver corps out of the 3, I think you're either splitting hairs, or really underselling Thomas. Thomas is an elite WR that was masked by the awfulness of the Georgia Tech offense and later Tim Tebow. He's every bit as good as the other elite WR in the game not named Megatron or AJ Green (yes, he is the equal Andre Johnson / Larry Fitzgerald / Roddy White). Manning isn't throwing to the NY Jets or St Louis Rams WR.
I think Brady has a slight edge on Manning for a few reasons:
Performed better in this harder schedule
Out performed Manning in the head to head (disregarding some garbage time yards)
but the big one: Brady is easily the best player on what looks to be a top 3 offense ever. This isn't 2007 where he has Moss (and I love Welker, but this years version is a far cry from even last years version). He's doing this despite a rag-tag offensive line, and an offense that had to be changed as early as week two because of the Hernandez injury. The only guy that has been steady on now a 4th 500 point team is Tom Brady.
Manning's had a great year, but I don't know how an objective argument can be made for it being better than Brady's.
Also, one last thing; the run game. Yes, Brady has a better run game, but I don't get how that helps his stats. The team has 20 rushing TDs (including 3 by Brady) -- change even 5 of those to passing TDs and Brady's passer rating is now 107.6, and this is no longer a real discussion. DVOA accounts for this, and while QBR somewhat does it doesn't account for schedule difficulty.