There would've been no place to put him and he's too high priced to simply be a bench player. Sox had their outfield and DH set coming into the season so where would've you put him?
He's also an exceptionally one dimensional talent. Yes, he hits plenty of HRs but he strikes out a ton. Yes, he's hitting over .300 right now but I'm willing to bet that by the end of the season, he'll be back towards his career number there. Also, there's no way that Adam Dunn could effectively play the vast right field of Fenway Park.
I don't know about his average at the end of the season, but obp is more important and he tends to do well in that category. Also, strikeouts are overrated.
In regards to Papi's struggles, people are saying NO ONE could have predicted this, but from what I read, the Sox front office was concerned about him this winter and his slowed bat speed, which would probably explain their reported interest in Dunn.
I do agree that a player of Dunn's caliber, probably wanted a guaranteed starting spot, so to sign him we would have had to pay more than Washington and convince him that he's have plenty AB's backing up numerous positions. He could back up Papi at DH, Drew in right, Bay in left, probably backup up Ellsbury with Drew shifting to Center, and if he was capable of playing first he could back up Youks or Lowell (with youks shifting to third). So he could of had plenty of AB's and you could also bill up the fact that Fenway is more of a hitter's park than Washington's.
IMO I think the reason the Sox passed is because Dunn has been against playing first in the past and the Sox went with their heart and hoped for a Papi rebound, despite the reports of slowed bat speed. They definitely didn't pass based on batting average or strikeouts. Those aren't the kind of stats they focus on. They know Dunn is a very good hitter and they might be regretting not pursuing him harder since he's tearing the cover off the ball (in Washington even), Papi looks like a shell of his former self and based on injuries.