And which proves more accurate long term? As in better than 50%.
Accurate for what? That's not even the appropriate question. The question is: given something complex like the economy how does one seek better understanding of it.
By collecting empirical data and trying create mathematical models to back test against the data?
Or by logical deduction aka praxing aka philosophizing?
It is an assumption that there can be a mathematical model underlying economics of course. You have to be aware of that.
In fact, you find the same in theoretical physics. There is an assumption that nature can be described by a mathematical model. That assumption is not empty, and evident. It is an axiom, that could very well be proven wrong. However, in theoretical physics, down to a certain level at least, one finds empirically that mathematical modeling works very well.
Now, the Austrian school maintains that this axiom is not valid for economy in the long run. Most other economists claim the opposite. However, contrary to theoretical physicists, they have never come up with a WORKING mathematical model in the long run. In the short run, they have. In backfitting data, they have some success. But in actually making predictions, economic modeling is - to say the least - much less successfull than physics in, say, predicting the next solar eclipse.
The answer is that the system is too complex. Right. The answer can also be that the Austrians are right of course.
There are other human endevours which are obviously not apt at being modeled mathematically. For instance, the plot of the first movie that will come out in the theaters in 2028. That plot is unpredictable by any means using mathematical models.
I'm not talking about determinism. There's not even a stochastic model that could describe the ensemble of plots of the movie that will come out in the theaters in 2018. The best one could do is to make a statistical description of past plots. But nobody knows if that statistical description will be valid for movies in 2028.
Nobody will find it ridiculous that there is no such mathematical model, and that it cannot be found. In fact, rather the other way around: people proposing to model this will rather be considered crazy.
With economy, however, the axiom that economic activity in the long run is following a mathematical model is an axiom taken for granted.