There are a lot of things that are missed with these 2 examples. Both Brady and Manning only ran 1 offense their entire career and by definition, both were "system QBs." When Manning went to Denver, the Broncos ran the same offense that he ran in Indy. When Tom Brady went to Tampa, he could not effectively run Bruce Arians offense, during the bye, elements of the NE system was implemented and by the next season, the offense looked nothing like a Bruce Arians offense.
Tom Brady 12 games before bye: 275ypg on 64% completion. 28TDs/11 INTs 95.1 passer rating
Tom Brady 4 games after bye: 333ypg on 69% completion, 12TDs/1 INT, 126.9 passer rating (having AB, who was familiar with NE's system didn't hurt)