Measure success however you want, but only one of the those two QBs seems to show up when it counts.
You do know that their postseason stats are very comparable to each other, right? (Outside of things that are team accomplishments, like wins, that aren't a good measure of individual performance.) Manning has a little better completion percentage and yards per pass, while Brady has a little better TD/INT ratio. (Although if you take out one outlier 6TD game for Brady even that's basically close to even.) If people are going by postseason success as who "shows up" they would have to go with somebody like Drew Brees or Kurt Warner. Funny though, somebody like Brees only has one Superbowl win and only played in 9 playoff games despite being dominate in both the regular and post season. It also kinds of shows how ridiculous it is to put too much emphasis on such a small section of games. Heck, even people like Bart Star, Troy Aikman, or Terry Bradshaw could be made to look better than Brady by that standard which is ridiculous.
Now if your assertion is that the New England Patriots have generally been the best team in football all around for the last 15 year span or so, and have been as close to a dynasty as modern pro sports will allow, especially in football, then I can buy that. That and having the benefit of actually playing teams worse than them in the playoffs most of the time is probably more the reason people would give them the benefit of the doubt than anything, if they are thinking semi-logically anyhow. Even then a gigantic portion of their success was luck like it is for almost anybody, and them even more so. All the other stuff is just inventing a creative narrative around things that sound good to the person making them without actually thinking objectively about it.