Rodgers is a great QB and will end up in the HOF, but as BB says, there's no quarterback I'd rather have than Tom Brady.
Rodgers has lost a lot of close games throughout his career. Some consider him too conservative with the game on the line.
Some of the stats bear it out. The Packers under Rodgers are 9-26 in games tied in the 4th quarter or OT. He's 5-24 when he has the ball in the 4th quarter down by 8 points or less, second-worst in the league to Cam Newton (stats as of 2013). The link does point out 7 of those 26 losses did have Rodgers scoring a go-ahead touchdown, only for the defense to lose the game, but even without those 7, it's a 9-19 mark.
Then again, his splits in the 4th quarter of close games are great, so it isn't necessarily entirely on him. But he's only led 8 4th quarter comebacks and 12 game winning drives in his career, or roughly the same as Mark Sanchez. Part of that is the Packers dominating while the Jets play a lot of close games, but part of it may be something else.
This article from FiveThirtyEight shows the incredible and confounding of Rodgers in the same space. He's actually quite amazing at 4th quarter drives to tie or take the lead (regardless of final result), better than everyone except Manning. At the same time, it talks about other scenarios and how Rodgers remains conservative even when down by 9+ (2 possessions).
Rodgers has NEVER led a comeback win with that margin, partly because he continues to play within the game. They compare him to Pay-me-a-ton only (not the greatest comparison), but Manning's INT % goes up from 7.9% when leading to 15.6% when trailing by 2 possessions, partly I guess to try and come back and win the game. Rodgers barely fluctuates from 6.2% to 8.1%, which is actually lower than his 8.3% in close games within a FG. He doesn't deviate from the game plan, and he has never come back from down 2 possessions in the 4th quarter.
You can make fun of Manning's INTs, but as Herm said, you play to win the game, and his gun slinging at the end has led to 14 wins in 49 games when down by 2 possessions in the 4th quarter. Meanwhile, Rodgers has gone 0 for 21 but kept a nicer stat sheet.
None of this makes Aaron Rodgers a bad QB. He's going to the HOF and deservedly so. But that last bit is damning. There's too much front-running going on, and considering we just won our 4th Super Bowl thanks to our HOF QB leading us from 14 points down TWICE in the division round and overcoming a historic 10-point deficit in the 4th quarter of the Super Bowl, I am happy to have our guy over anyone else in the league.