Babcock can give his two cents, and it's well established that the two disagree frequently, but Holland has ultimate say on all personnel matters.
So no, I don't think Babcock is equally responsible for lack of moves. He doesn't have the authority to make trades or offer contracts. How could he possibly be just as responsible? It's literally not his responsibility.
Where has it been established the two disagree? I don't remember hearing that other than on LGW. I've always thought Babcock has a lot of influence in the organization because of his status as a top coach in the league.
In any case, Babcock is responsible for crappy line combos and not making good adjustments. Playing Abby on the top line and Legwand on the 4th line is laughable. Legwand is a solid player who could contribute, instead he's paired with Glendenning and Miller.
According to my profile, my reputation is excellent. LOL.