Welcome!
I just went through a huge debacle on Facebook with a similar truck and post lol.
Back in 05, I went down, checked out a nice, used, 2500HD, shortbed, extended cab, 6.0, sweet truck. I make a deal, buy it, take it home, life is good.
The next day, I get up, load up my truck bed camper, trailer, quads, gear headed to northern Michigan. That thing hunted between 2-3-4, it was absurd. I'd go up a hill, wham, down to 2, 4000 rpm, bang 3.... can't hold it, second again, speed dropping, ooop up the hill, lug back into 4th.
That truck went right back to the dealer and I swapped them for my crew cab long bed with an 8.1 and an Allison, no more problems towing, I can hold 4 or 5, the entire trip, which is mostly 2 lane roads at 60 mph, so it's barely idling. The 6.0 towed worse and needed more RPM than the 350 it replaced.
Now, yes, the 6.0 moved the load. Hauled it, didn't poop, it was fine. Probably would have continued to be fine if I were the type of guy to just crank up some Katy Perry and set the cruise and sing along oblivious to the world, but it was not what I'd call an enjoyable experience. Also, the 4L80E compared to the Allison when towing is just a piece of trash.
I wouldn't even consider a 5.3 or a 4.8, cammed, tuned, boosted for something that's going to really tow.
I imagine, most people who tow, tow like me, maybe twice a month, some recreational stuff, a camper, boat, ATV's, whatever. The rest of the time, they're just driving around alone probably going to work or whatever. So I guess that's the real question, how much are you truly going to tow, and how often?