I'm not sure why you asking me this question? Clearly I think WAR is a better indicator, but I question the validity of a certain organization's calculation of WAR when the difference in ERA is as extreme as it is.
The difference between b-ref WAR and fangraphs WAR is that B-ref gives a more accurate indication of how the pitcher has actually performed that season. While fangraph's WAR is more of a predictor on future performance. So fangraphs is more speculative rather than an accurate portrayal of his actual performance.
Not really unless you believe giving the pitcher credit for things he cannot control.