Offensively, they are pretty much the same. Defensively, I don't really trust one over the other, but it's not true that B-Ref does not update their defensive stats. They take their defensive stats from the Fielding Bible which regularly updates their methods.
Since I use stats more for evaluation of past performance than for prediction, I like B-Ref better for pitching. If one is going to attempt to project pitching, you are right that f-WAR is better. However, pitching is so unpredictable that it's hard to say how meaningful that exercise would be. Even the projection expets like Szymborski can't do it well.
I have given up on B-Pro. They don't provide anything I need that I can't find on B-Ref and FanGraphs and the latter two are easier to use. Plus, B-Pro charges money to read articles about new advancements and I have reached my limit on subscriptions for which I am willing to pay.