The original question (how much better...?) remains unanswered. Indeed, it only seems to have raised more questions. The main reason it remains unanswered is that nobody (myself included) really knows because nobody cares enough to try and find out. At least this is one reason. Another is that the test might get sidetracked.
Imagine a scenario where our propective tester decides to test this. He has to use a good barrel because, as I'm sure all will agree, it matters not what kind of chamber you use; a bad barrel ain't gonna shoot. So, he orders a match grade Shilen barrel in a twist he likes and in a match contour he wants. He carefully fits it to a proven action and chambers it with a minimum dimension reamer with a tight neck ( say .334") he turns some brass to fit and loads up an appropriate amount of 4895 and a 150 to 168 grain bullet from Berger or Sierra. It will probably group five into .3 moa or less. In fact, sub 1/4 moa isn't impossible. At this point, our tester is going to have a difficult time convincing himself to rechamber to see if he can screw this fine shooting rifle up. So, the test never gets completed and there is no hard data.
In lieu of hard data though, we have what amounts to hundreds (maybe thousands) of man/years of experience with the 308 in everything from unlimited BR rifles to full bore target rifles to longrange match rifles to hard used hunting rifles. This combined experience tells us that our tester could probably have enlarged the neck of his chamber and seen very little effect on accuracy. Not until he enlarged the throat would he start to see any real deterioration. Even then, as lond as the chanber remained straight and concentric, accuracy could still have been classed as better then good. He might have had to have made some adjustments to the load but the rifle would still have good potential.
Our experience tells us, if the rifle is a light weight hunting rifle, the chamber is not going to be that critical. Our experience also tells us, chamber dimensions will not, if reasonable, make or break a rifle. Chamber quality; that is to say, straightness, concentricty and, perhaps, throat configuration, will have a much greater effect.
Alan Warner mentions that he has all kinds of variations on hand for various bullets etc. and they work well. The truth is, any of the chamber variations would work very well if the rifle came from his shop (or the shops of many of the accuracy specialists on this board) because the important aspects of the rifle would be well taken care of. Put the rifle in the hands of any of the top twenty or thirty shooters on the line and it won't suck! Put it in my hands, it might be a different story. Regards, Bill.