Phenomenal write up, @21isSuperman
Good points, @GoPats
To me, two things made the difference in favor of Brady:
i) Turnovers due to Brady's better arm resulting in more incompletions than INTs compared to Peyton
ii) QB sneaks in critical times to keep the chains moving on 3rd and 1 or 4th and 1. Those resulted in better time of possession for Brady's offenses, and reduced chances for opposing offenses to have short fields in the case of the Patriots.
However, in defense of Peyton, here are other points to consider:
i) With Peyton (and Luck) going to teams that desperately needed help getting back into the playoff picture, it infused a tendency of having to do more by themselves which result in more turnovers from the QB position. When Brady was not nearly the QB he was now, he could ride a D with many HOF'ers that were great scoring Ds too, and figured out he didn't have to force the issue. Once he became a better QB, those lessons were retained well and he could pick and choose spots to take risks as his career went on.
ii) Special teams - Brady enjoyed outstanding special teams play when compared to Peyton's teams, poorly constructed from the 40th-53rd player, IMO, by Polian, were bottom dwellers in special teams field position. That hurts any offense's ability to put up points consistently, let alone against stellar Ds you face in the playoffs (whether it was a Dante Hall KR TD in KC he had to overcome or Ellis Hobb's returns in the 2006 AFCCG he overcame or Scifres punting show in San Diego or Hester return TD in SB he overcame or onside kick recovery in SB or even Peyton's last game in Indy vs Jets where a 53 yard KR was given up to Cromartie, these are just playoff examples, us Colts fans really suffered more during the regular season). Those things matter in close games to swing momentum and Peyton felt he had to do more consistently because of the lack of a well rounded team.