My opinion:

I believe that good barrels have a place in handgun accuracy, but not to the extent that they do in rifles because of the way we shoot our handguns.  If we regularly shot at 50 yards and more, the barrel would take on more importance.

To me, the most important aspect of handgun accuracy--and I mean internally, not the shooter, which is always the final key --is repeatable positioning. 

A side comment is called for there.  Modern 1911 pistols bring nothing to the accuracy table with what you referred to as "go fast stuff."  That stuff is simply intended to make the gun more shootable for the shooter--sometimes it works, sometimes it doesn't.  But it doesn't affect accuracy in the way we mean it.

Lurkers, accuracy comes in two flavors, mechanical and practical.  Practical accuracy is the accuracy the shooter can coax from a firearm with the given sights, trigger, ergonomics, and so on.  for example, you are far more likely to hit your target with sights you can see and line-up than with those you can barely align. 

Mechanical accuracy, which is what we're discussing here, is the ability of a given firearm to produce tight groups in and of itself, and is based on factors such as a quality barrel, barrel fitting, and repeatable positioning when the pistol is in battery as mentioned above.

Returning to modern 1911s.  "Go Fast Stuff" is meaningless as it concerns mechanical accuracy, my interest here.  What modern 1911s do have is fitting using CNC-machined parts, which are far better than parts of old before we had the precision of computers, and required more hand-fitting.  Often an assembly line didn't take the time to fit barrels, links, and bushings well enough to eek out maximum accuracy, in fact they often only got them so they would function--and then only after a fashion.  Today 1911s will function 100% and often the accuracy is superior.  The more you spend the better the accuracy, as a rule of thumb.  But it has nothing to do with doo-dads or fanciness, it has to do with what's inside, stuff no one ever sees. 

A 1911 is capable of one hole accuracy at 25 yards, even with the Colt/Browning falling barrel action, and this is what I'm interested in comparing to the Walther wedge-locking action.  Based on experience with the Beretta 92, comments here, and Harvey's sensational group shown in his message, it appears the Walther action is also equally capable of outstanding accuracy.

I wonder if the reason the Browning action is much more commonly used is because it is simpler or cheaper to produce, or for some other reason?  I have the impression now that accuracy is unlikely to be the reason.