I think it's understandable why some people think Brady is a system QB, just like it's understandable why some people think Manning is a choker. But in the end, both viewpoints are wrong as there is plenty of evidence to back it up both ways.
There is so little that separates the greatness of the two, that it's not even worth debating anymore. They are pretty much equal when all factors are considered. You really can't go wrong with either one, and there is basically no situation in which one has a decided advantage over the other. Both can tear up any defense imaginable, make fantastic reads and audibles, and are scary as in the clutch. We all know what Brady has done in the clutch with a number of game winning drives in the playoffs and SB, and Manning is so scary that he made arguably the greatest coach ever (Belichick) make a generally unthinkable desicion because he was scared at the thought of Manning having the ball with the game on the line.