I think this article omits the most important distinction between Bayesian and Frequentist statistics: subjective vs. frequentist interpretations of probability. In my own opinion, neither is "true", they're both just different tools for different purposes.
Bayesian inference is great when you have to make a decision and there are many theorems that illustrate this (for example, the arguments around coherence [1] and the complete class theorems [2]). In fact, Bayesian techniques are often useful for creating estimators with great frequentist properties! However, Bayesian interpretations of probability, and thereby the meaning of Bayesian statements, are inherently tied to the beliefs of an individual. That means that Bayesian statements usually aren't "true" in the objective / non-relative sense that we often expect from science. On the other hand, frequentist statements tend to have more of an objective flavor. The trick is: all our mathematical models have short comings and ways in which they're wrong when applied to any particular situation -- so neither really has a claim to being true.
The frequentist perspective often looks at worst case risk and tends to give a more global understanding of a procedure in terms of "how does this procedure shake out in all reasonably possible scenarios?". So, frequentist methods tend to be a bit more risk-averse which is often useful but can cost you for being to pessimistic. Ultimately, the real win is to know your tools well and to pick the right one for the job.
Bayesian inference is great when you have to make a decision and there are many theorems that illustrate this (for example, the arguments around coherence [1] and the complete class theorems [2]). In fact, Bayesian techniques are often useful for creating estimators with great frequentist properties! However, Bayesian interpretations of probability, and thereby the meaning of Bayesian statements, are inherently tied to the beliefs of an individual. That means that Bayesian statements usually aren't "true" in the objective / non-relative sense that we often expect from science. On the other hand, frequentist statements tend to have more of an objective flavor. The trick is: all our mathematical models have short comings and ways in which they're wrong when applied to any particular situation -- so neither really has a claim to being true.
The frequentist perspective often looks at worst case risk and tends to give a more global understanding of a procedure in terms of "how does this procedure shake out in all reasonably possible scenarios?". So, frequentist methods tend to be a bit more risk-averse which is often useful but can cost you for being to pessimistic. Ultimately, the real win is to know your tools well and to pick the right one for the job.
[1] https://en.wikipedia.org/wiki/Coherence_(philosophical_gambl...
[2] https://projecteuclid.org/euclid.aoms/1177730345