I share many of the concerns raised here about Peterson's off-field issues, his potential contract, and his fit (my understanding is he struggles running zone, from shotgun, or without a fullback, and he had seven fumbles in his last full season), but two points in his favor:
1) For some reason we seem to have a one-year timeframe when it comes to football evaluation. In 2015, Peterson was the best running back in football, leading the league in rushing, averaging 4.5 YPC, and being named first-time All-Pro, while Blount ended the season on IR. Last year, Blount had a career year while Peterson got hurt early. Obviously we can't handwave away 2016, especially with Peterson just turning 32, but it shouldn't be any mystery if the Patriots (or any team) prefer ADP to Blount. His resume is far more impressive, and he was extremely effective just two seasons ago.
2) Something I noticed a lot in 2016 was the Patriots running Blount outside while the WR crackblocked inside, forcing CB to try to tackle Blount. This is a great counter to teams that flood the middle to take away the slot / TE passing game, matching up the massive Blount on corners. Of course, he had to get to the edge to make this work, no sure thing. Blount's considerably bigger than Peterson, making him perhaps even more intimidating to DBs, but Peterson's certainly got a lot more speed to make this approach pay off more consistently.