I offer the following as an alternative to the sort of analysis provided above.
Brady-Era Patriots
Combined rank (rushing TD, points allowed)
bold = 10-win season
2001 7th 11-5
2002 23rd (Brady started every game) 9-7
2003 13th 14-2
2004 6th 14-2
2005 17th 10-6
2006 4th 12-4
2007 4th 16-0
2008 9th (Brady missed season) 11-5
2009 7th 10-6
2010 9th 14-2
2011 12th 13-3
2012 7th 12-4
2013 6th 12-4
2014 10th 12-4
The only year they failed to win 10 games, and the only year they didn't make the playoffs with Brady was 2002. There wasn't any problem with Brady that year, the Patriots just weren't a good team. Every other year, the Patriots were at least an average team, and usually a good-to-great team. Every other year, the Patriots had at least 10 wins. Even in 2008 when Brady was injured in week 1 and missed the entire season, the team went 11-5.
It's the same story -- just not the one you think you're telling.
Montana-Era 49ers
Combined rank (rushing TD, points allowed)
bold = 10-win season
1981 6th 13-3
1982 20th (Montana started every game) 3-6
1983 7th 10-6
1984 2nd 15-1
1985 3rd 10-6
1986 8th (Montana missed half the season) 10-5-1
1987 12th 13-2
1988 8th 10-6
1989 8th 14-2
1990 10th 14-2
Team matters, perception doesn't.