Just 3 years apart, but humoungous changes. In 2016 a new SS, 3B, 1B, LF, CF, RF, and C plus an entirely new rotation of Price, Porcello, Wright, Pomeranz, and ERodriguez. 2013 team had a new but well respected manager named John Farrell, but in 2016 we are stuck with a loser ( 2014 and 2015) named johnfreakingfarrell who insists on abusing and misusing his bullpen, who had the temerity to play Young in LF against righty pitchers, who allows his players so much freedom on the basepaths they are continually getting picked off or thrown out trying to steal or advance when it's inadvisable, who is clueless on when to take a starter out, ditto on putting together a lineup card.
Nevertheless, despite the liability of a loser manager and an astonishing turnover of position players and starters, the 2016 team is now in first place in the AL East and has a real shot at the playoffs. With 93 games played, they are 15 games above .500 with 54 wins and 39 losses. The 2013 team at this points was 56-37, 2 games ahead of the current Sox. The 2013 team had better pitching but surprisingly, were still ranked 14th in MLB in ERA, whereas the current Sox are 18th in MLB in ERA. The 2013 team, however, was about half an ERA better. Both 2013 and 2016 led/lead MLB in runs scored and OPS, but the 2016 team has a higher OPS and should outscore the 2013 team by a bunch. Fielding-wise, I'd called it a draw: Bradley>Ellsbury, Betts=Victorino, Holt>Gomes, Napoli=Ramirez, Pedroia 2013>Pedroia2015, Drew>Bogaerts, Shaw=2013 conglomerate, Leon>Salty.
Overall, I have to give the edge to the 2013 team because their pitching, with a cumulative ERA of 2.00, was just unreal in the playoffs. Nevertheless, this team, like the 2013 team, is a lot of fun to watch.
Feel free to disagree.