You mean one of these?
The point of the bull barrel is to make a HEAVIER barrel than standard. Getting rid of the bushing is more of a side-effect of making the barrel walls thicker. Cone barrels are basically the same as bull barrels, except that they are somewhat lighter, since they taper back from the muzzle evenly instead of being thicker for most of the length of the barrel.
Why make a heavier barrel? The main purpose is to reduce muzzle jump and felt recoil, without the increased muzzle blast and decreased muzzle velocity that porting or compensators would cause. Bull barrels are popular in USPSA/IPSC (and restricted in IDPA as an unfair advantage) for that reason.
As a practical matter, bull barrels are also used in sub-4.25" 1911 barrels because it is easier to make itty bitty guns work right with a bushingless barrel. The shortest 1911 barrel you will see with a bushing is usually 4.25". In that case, the bull barrel is just a practical solution to the problem of getting the gun to work at all.
You can also argue for some theoretical advantages of the bull barrel. It should heat more slowly (greater mass) and cool off more quickly (greater surface area) than a standard barrel. The extra mass should lead to slightly delayed unlocking, which would be beneficial in guns running higher pressure cartridges. Bushings DO break on rare occasions, and a bull barrel eliminates that part entirely. The barrel itself should also be stronger and more rigid than a conventional barrel due to its greater mass and thicker barrel walls.
I've had basically the same type of gun (10mm Delta Elite), 1 with a bushing barrel and 1 with a bull barrel. My opinion is that bull barrels make a small but noticeable difference in felt recoil and muzzle jump. I wouldn't put them in the same class as, say, full length guide rods, since they make an objective difference (hence IDPA not allowing them in >4.1" guns as an unfair competitive advantage) and serve a definite use in making smaller 1911s actually somewhat workable.
Incidentally, you DON'T "need" to use a full length guide rod with a bull barrel, but almost nobody does a bull barreled 1911 without one.