Did anyone ever wonder why Savage and Remington's 788 (among the cheapest guns ever made) are also among the most accurate? Is it because they screwed on Hart barrels?.....not a chance.....
Barrel quality is far far over worked as a factor in accuracy.....Now if one wants the difference between a 1/4" group and a 3/16" group one of these makers might be a tad better. However the most of us will be hard pressed to tell the difference between an off the shelf savage barrel and the finest Hart (or other) ever made.
The fitting of the barrel to the action is also critical and many other factors.
If you are a serious bench rest shooter the barrel to pick just might be one of the mentioned barrels. If you're a hunter or varminter the barrel that is best just might be one from A & B or ER Shaw....personally I have used Douglas with excellent results.....but don't get the mistaken opinion that one can buy accuracy just by buying a premium barrel.....You will still be hard pressed to beat some of the elcheapo rifles from Savage......and some of the former Remington 788s