If I had to simplify it, I would say the key success factor is credible executive-level judgment. By the final round, firms usually assume you can handle many of the basics.
What differentiates candidates is whether they sound like someone who can think clearly, communicate crisply, and make sensible calls under uncertainty.
That does not replace structure, math, or fit. It is more like the higher-level quality that sits on top of all of them.