1, maybe 2.
When you have an elite team around you, you are bound to win at least 1 in this span of time. Better clutch QB's step up more often resulting in more rings. For each of our rings Brady came through big in the clutch - in 2001 it was the Super Bowl drive to FG in 1:20 with no TO's. In 2003 it was his monster performance vs. the Panthers when our defense gave up 29 points. In 2004 it was another brilliant performance in Pittsburgh against the league's best defense. Manning has only had one performance comparable to this, in the 2006 AFCCG, which resulted in his lone ring.
Aside from 2001, 2002, and 2006 Manning would have had a contendor quality supporting cast as our QB, but he wouldve blown at least 2 of them. The supporting cast he had in Indy in 2005 and this year were pretty damn good and he didnt take them past the divisional round, whether it was his fault or not.