This really is a bad post, but I just wanted to highlight this portion.
Game winning drives, NFL career:
Tom Brady, 36 (ranked 6th all time)
Fourth quarter comebacks, NFL career:
Tom Brady, 25 (ranked 10th all time)
I WILL say that Tom Brady has not been good at all in recent must score drives, but the man built his entire reputation on being 'Tom Cool' and never giving up.
I've never seen Tom Brady lose his cool in a crunch time situation, and I'm pretty confident the only thing you are referring to is when he looks for a flag (specifically the Ravens game where he got one), which every NFL QB does.
I never really choose between Tom Brady and Peyton Manning, because it's pretty impossible to make a case for one being better than the other. Peyton has surprised me this year; I thought he had no arm strength, and his throws have been wobbly, but they have gotten there when he needs to get them there.
Trying to choose one over the other would either be a case of homerism (Glen), or an obvious disliking (rams) for the player.