The advantage will be less poi shift across a range of various projectiles (within a given size and weight range that is suitable to the barrel twist, bore, ect) and less poi shift across various power levels. The barrel will be easier to tune, and more forgiving. But a thin barrel that has lots of flex can still be very near just as accurate in my experience. I've had extremely good results with my 700mm fx superlight barrel which is just a thin liner floated on 3 small spastic rings with rubber on the outer edge riding in a thin aluminum shroud. Granted, it did not shoot as well with any moderator I used, even tiny ones. It (a 22 cal barrel) would stack 36gr slugs at 100 yards just under 1/2 moa. I'm sure maybe a bull barrel could do slightly better, and this might be magnified at longer ranges. But that just isn't my cup of tea. I converted that barrel (still have the parts) over to 500mm and prefer shooting much lighter slugs at higher speeds. And at shorter distances.
Now, if you're into competition and what have you, or extreme long range... It may be worthwhile. But there are a lot of other factors that need to be accounted for and applied correctly.
In whatever arena I have interest, the added weight is by no means worth the tiny gain to be had. I'd rather have a thin barrel in a carbon fiber tensioned shroud. This setup in a way emulates a bull barrel. And is way way way lighter. I have one such barrel on an unregulated rifle, and found it was actually necessary to overcome the varying harmonics that occur as pressure at the valve drops, and valve/hammer interaction changes resultingly. The rifle came with a tensioned barrel, but a heavy metal shroud instead. The barrel in it now is much shorter, of a different caliber, and bonded to a carbon fiber tube as well to further stiffen it prior to tensioning.
A lot of FX guys now use this practice as well of using a carbon fiber sleeve to stiffen their liner inside of the shroud. Fx also has some tensioning kits for the impact at least.... IIRC?