I think it's wrong to assume that non-empirical methods can be reliably trusted to give better results. Humans are terrible at avoiding bias or evaluating risks, especially for uncommon events.
Food for thought: if every method for predicting event x is terrible, then you might as well not try to predict x and build your life in such way that you never expose yourself to the risk of x happening.
From a Bayesian point of view, that amounts to a "prediction" that the probability of event x is so significant that you should build your life around it. But I guess if you knew enough for that sentence to make sense you wouldn't have posted your comment. So, suffice it to say that Bayesian decision theory cuts the knot you're talking about.