The right barrel and set up properly any of them will win.
There are features with the turbo and hall but the main is that you start off your benchrest rifle with an action that everything is square and machined to more exact tolerances.
From a cost standpont, you normally have to buy a complete rifle many times $700 to $1,000 and start tearing it apart. When you could buy a custom action for a little over $1,000 to start your build and the resale will normally be higher.
There are many pluses with all of the custom and what you call old school actions that make each of them stand out. But hopefully someone will jump in and give you more specifics.
For me personally, I want something easy and quck to load. My favorite is the Swindlehurst and the Anschutz 54 but since the Swindlehurst is no longer made so would probably consider a hall for the loading reason. But wouldn't think twice about haveing another Anschutz built if I had an action laying arounnd.
Charlie