If we are just going on my love of the teams and not the ultimate end result, 2010 was my favorite team.
They traded Moss a few games into the season, and immediately the uproar from the media began.
So many awesome young players that season, it was really confirmation of Belichick and Brady's genius. This was the first time a completely new roster post-SBs could completely dominate. There had been skepticism and doubt that after losing so many players from the 2001-07 era, their days of being really elite were over, and they could still win but would never be that type of superpower again. They proved everyone wrong.
Danny Woodhead picked up after the Jets cut him. Devin McCourty plays like Revis as a rookie at CB. Rob Gronkowski and Aaron Hernandez emerge. Deion Brach returns. Everyone they throw into the mix becomes a star immediately. That team was awesome. Tragic ending, but this was a 14-2 team with a bunch of scrappers and rookies. They challenged the '07 team for overall offensive efficiency with a bunch of no names.
At one point they were on a tear that I really thought was more impressive than 07. They were absolutely dismantling everyone. Smashed Chicago on the road. 45-3 beat down on the Jets. Set a record for most points at Heinz by opponent vs Pittsburgh.
I didn't really like the 2011 team...felt much different from 2010. I felt the 2011 team was almost a letdown and didn't have the heart and emotion of the 2010 team. Even had they won the SB, I never really connected with that team.
After that, 2004 and 2014 are tied for second. Those teams could win on the road against elite opponents and always played their best against the best. 2007 is really close, but I can't ever shake the disappointing finish.