Yeah I guess the easiest explanation is that they address different problems in different ways.
The problems are centering the axle under the jeep and correcting the arc of the trackbar which affects vertical movement of the axle. More angle=more arc=more side to side movement accompanying the up and down.
The adj bar only addresses getting the axle centered back under the jeep after you lift it and the arc of the bar swings the axle to one side and pushes it out of centerline. Adjust the bar out to center it back under and your inline again, but this does nothing about correcting the arc - ie. getting the bar back closer to parallel with the axle.
A bracket moves one of the bar mounting points to get some parallelism (like that? I just made that one up) back into the system. It also serves to help recenter the axle, since if you move the susp. 3", then move the bar mount 3", it should be back pretty close to the stock arc so the stock length should be groovy, which not only re-centers your axle but cuts some of the sideways arc out of the movement so it also cuts some of the axle shove when you hit bumps or dips that make the whole axle move up. The farther from parallel, the more side to side movement there is when the axle travels.
Downside to brackets- strength of factory welds.
the factory welds on the t-bar mount tabs on the axle have failed on a number of jks. When you use some types of the axle side brackets, you put more leverage on these welds and are probably more prone to breakage. BUT some of the manufacturers (ie. PolyPerf) have taken this weakness into account and built brackets that actually brace the mount and strengthen it. However to use them, you need to do some other stuff to make room - high steering mod, etc. The other option is to use a frame side drop bracket where the factory mounts seem plenty beefy to lower the frame side of the t-bar, which is what I did in the back. BDS makes one.
So umm yeah, I hope that explains what little bit I understand about the situation.