Moss came here with a reputation as a malcontent. When a malcontent is really talented, he can be a good risk in the short term, as a change of scenery is usually the best thing that can happen to them. It gives them a chance to disprove their bad rep. So they can give their new team a good season or two, before sliding back into their old ways. The key is to be prepared for this slide, and cut them loose before they drag the team down.
Moss gave the Pats one super season, followed by a decent one, but has been erratic since (and has been erratic so far this year). They waited four games to see if they had enough weapons to win without him, and figured they did. So they moved him to Minn. where he'll probably give them a great season or two. But the Pats' time to move him on was now.
They end up with a third rounder, which is what they paid for him in the first place (I think).