Chargers- better roster, great road team, play better outside of California. They literally have not lost a game outside of California this year (3 'home' losses and the 1 in their 7-1 road record was at the LA Coliseum.)
Other then Brady/Belichick, the Pats don't have any real roster advantages over the Chargers.
The only thing on NE's side is playing at home, (Brady has only 3 true road playoff wins in his career- 2 of them if you count Bledsoe's 2001 AFC-CG cameo) and their past. The Pats' mystique and aura, esp. at home, seems to be their greatest strength.
If the Bolts can win at Pittsburgh/Arrowhead/Seattle/Baltimore..... I don't think they'll be afraid of Gillette Stadium.
Chargers, as they did a decade ago at Indy, pull the early Sunday road upset.