I think it comes down to the fact that, if you want to understand the universe around us, the scientific method is consistently successful and supernaturalism is consistently a failure.
If you want to actually prove that scientific method is better, it's very hard to do without reasoning with the scientific method itself, which would be circular logic and thus inconsistent with the scientific method.
So let's just say that, I like to know how the universe works, and if any form of supernaturalism were the best way of doing that, then I would use it. Instead I use the scientific method, because that is what works.
Supernaturalism has other uses, but they are not uses that I subscribe to.
Einstein once asked "Did God have a choice in creating the universe?"
Implying that Einstein believed it was at least possible that the state of the entire universe could be derived from no sensory data what so ever.