Our communication in comments frames my answer, so it is reproduced here (emphasis mine):
I would like to know how you would like us to treat the phrase
"evidence is superior." For example, if we were to choose to do it
mathematically, we could declare there is a poset of such events,
ordered by the quality of the evidence. Then we could spend time
discussing what it means for one set of evidence to be "better" than
the other. As a crude example, one could argue that belief in God is
"superior" because it has been in use longer, and thus has had more
time to prove its worth. It is worth noting that your ordering may be
different from that of others. – Cort Ammon
That's a good question,
but I'm not sure I want to get more technical or "define away" the
question. I am thinking broadly of the standard validations of
"evidence" in science. Prediction, control, coherence, falsifiability.
Evolving along some Bayesian line. To which the history of science has
added a big dose of consensus or "paradigm" inertia. Big bang, like
god, is a "first cause" prior to any possible experience. Is this
problematic for the old standards of validation? – Nelson Alexander
By assuming a scientific stance, you have to understand that you will naturally arrive at an answer biased towards science's result. However, if we look at a slightly broader issue, I think there is still some room to breathe life into the counterargument.
Let's look at the underlying assumptions. After all, belief in a big bang is really a result from our mathematical models of the universe, and belief in God is really a result from the reading of the Bible. So let's dig at the underlying tricky axioms that neither outlook really likes to look at. Science, with its mathematical models, explicitly assumes that the "laws of nature" are invariant. The laws of nature you experience within your lifetime are the exact same as were experienced in the era of Jesus, and all is explained with those laws (or at least "most" is explained, depending on how hard lined your scientific stance bends towards deterministic physicalism). What evidence do you have to defend this? Well, the laws haven't changed during your life, or you'd have noticed.... right? Well... maybe? Sort of? Did you ever feel Deja Vu? Perhaps the Matrix changed when you weren't looking? Such troublesome questions are the subject of a great deal of philosophy, and worth reading into if those questions are interesting to you.
Likewise, a belief in God typically is deeply entwined with a belief that the Bible is Truth. What evidence does one have to defend this? Well, the wordings vary from individual to individual, and there's fair argument that they should vary. However, it turns out that no assumption they have to make is any less defensible than the argument that just because we've never perceived the laws of physics change doesn't mean they change (you happen to mention Bayesian statistics... Jeffery's Prior deals with this frustrating aspect of Bayesian thinking, at least as best as can be done).
So, in the end, whether the evidence for one approach is better than the other is highly subject to the particular metrics you choose to apply to it, from a "truthyness" perspective. If I may expound, I would argue there is another metric which one might use instead: how does the application of this belief improve your life? Both outlooks have very intriguing ways to improve your life, and they differ greatly. Many would not trade God for Science, and many would not trade Science for God. There may be something to both. It might even be worth one's time to explore them both!