We don't really know what the decision ladder is--the media doesn't talk about it. Cherington being a young GM, you can be sure Lucchino is right over his shoulder. He doesn't breathe without a nod from Larry. Clearly, though, Henry has been stroking Ben, since the media got the word Ben gets the credit for the Dodger deal--though Henry actually made the deal with the Dodger President Kasten at the owner's meetings, as reported in some detail by the national media. I think, however, the FO deserves some credit for picking the prospects that came to Boston. It's pretty obvious a deal of that magnitude and money is made at the ownership level. As for trades and FA signings, Ben has some help in the FO this year (James et al); Lucchino and the higher ups probably sign off on any deals as well.
The real conflict traditionally is between the GM and the manager. Last year, clearly V had no say. Tito probably had little say as well. I suspect Farrell has a lot more say--he's highly thought of by the higher ups. The question is who has the final say in personnel, lineups, starting pitching, the way the BP is used, etc. These things are not discussed by the media.