The controversy is decades old and largely resolved. Both methods work well on large enough data sets, Bayesian methods are far superior on small datasets
It is ultimately the same math, if you are comparing apples to apples. Just different ways of looking at a problem. Sometimes one is better suited than the other.
It’s like as if physicists were arguing over whether Cartesian or Polar coordinates were better. It’s the same damn physics, just expressed differently. In some problems one approach is easier to work with than the other, and can even make seemingly intractable problems solvable. But that doesn’t mean the other approach was “wrong.”