How much of a noticable difference is there between the 200 action and the varmint or target action?

Obviously the triggers are different and the Savage actions have more material, different ejector styles but what will that translate to in the real world?

For example:
If you were to build a 6br with a decent aftermarket barrel and stock, good glass, for shooting at 600 yards.
Everything else being the same what accuracy difference would you see by using the different actions?