The 5.3 came out as the 350/5.7 replacement. The 6.0 was their big motor for the HD's, 1500HD, 2500HD, 3500HD. Then in the early 2000's GM came out with the 8.1 for the HD's. I am not sure but somewhere in the mid 2000's GM dropped the 8.1 to meet EPA emission standards fleet wide. The 6.0 became the only gas engine available for the HD's. It is a great motor, not a big block, but it is a workhorse and very reliable. I have had a 2003 1500HD with the 6.0 and 4 speed transmission and a 2010 2500HD with the 6.0 and a 6 speed transmission. Both have been extremely reliable. With what I have towed I wanted a 1500/2500HD, but I did not need the diesel. The 6.0 does have its limitations depending on what you tow, but it is a very reliable engine. It does love to drink gas!
My brother in law still has a 2002 2500 Suburban with the 8.1 that he bought new to tow his Airstream. I once met a man at a gas station who had a 2500HD pickup with the 8.1 and an Allison transmission, he said he was never going to sell it. You could not get the Allison transmission in the Suburban, supposedly it would not fit.