I think the "improvement" of a single shot action can only be seen when everything else is done first.
If you are building a Bench rifle, or a 1,000 yard rifle, and have a top quailty barrel, best of reamers, and top of the line gunsmithing, then you will probably see 20%-ish improvement.
But on guns that are less than state of the art, that 20% gets lost very fast.
When you are talking about factory, or "semi" custom varmint rifles with mid-range priced barrels, you can have repeaters that are more accurate than single shots, because there are too many variables that enter the picture.
And... if you are going to use the rifle in the field (not benchrest) then that 20% is lost, and you should shoot what fits your target and circumstances and not worry about it.