Schneider has had to deal with the same type of rotation issues that Charlie dealt with. White really hasn't been any more effective than Kikuchi, and Berrios has continued to be incredibly inconsistent from start to start as well. I won't argue that the bullpen is far more reliable now, as we are no longer subject to a parade of sub replacement relievers being utilized in close games because nobody more effective is available.
We aren't privy to what was going on behind the scenes. From the comments we have heard from Atkins and the players themselves there was something going on which necessitated the managerial change. Whether Charlie simply couldn't handle the pressure of a close pennant race, couldn't help rally his team around the Budzinski tragedy, or had some other sort of issues in the clubhouse we didn't hear about it was rather clear that he had lost the team. I don't think it's a coincidence that they have performed better after the managerial change. This could certainly have been a result of the players simply stepping up and performing more up to their abilities, but the fact remains that there is often a very fine line between winning and losing in baseball. We have seen more than enough differences tactically in game which has directly contributed to the team winning more games. During a game the manager is responsible for placing his team in the best possible position to win games, and I think that Schneider has been far more effective with his in game decision making than what we saw under Montoyo.