I think they will certainly be better this coming season simply because they have Steve Kerr calling the shots instead of Mark Jackson. Kerr will get more out of Bogut, Lee and Barnes imo. He has already stated that he wants to use Bogut much more on the offensive end than they did last season. Jackson practically removed Bogut from the offense completely, which is stupid, as Bogut has legit low post skills, a good shot, and is a great passer. Using him to establish an inside game will open things up for Lee to get more offensive boards, and will lead to better looks for Curry, Thompson, and Barnes.
Barnes was misused by Jackson last year as well. He has some excellent offensive skills, but is not adept at creating his own offense, which is what Jackson tried to do with him and lead to Barnes totally losing confidence in himself.
The Warriors will take the next step because they have a decent coach finally.