Have you looked at the springs? Certainly any engine & rear combo in this HD (6.0 & 4.10?) should move the weight, but the weight distribution over the springs might be the issue. Its also possible that the springs could be upgraded if they are not up to the job.
I have put this much weight in the 6.5' bed of my 01 Silverado LS Ext Cab 1500 z-71 (5.3 & 3.73) and I would not want to do it often or at highway speeds. Of course, the trucks you are comparing are more HD than mine. Towing far more weight is easy.