I tow with both versions of transmissions in nearly the same trucks.
My '01 Ram Cummins with an auto
Dad's '02 Ram Cummins HO 6spd
'98 GMC C30 454/NV4500
'76 C30 454/th400
I've towed the same stuff behind all four vehicles, so I've had lots of chances to compare the auto vs. manual under load behind BOTH a big block gas engine and a turbo diesel.
Here is what I've come up with. I like the manual behind the BBC, a gas V8 is snappier than the diesels and really gets up and goes with a manual. Better fuel economy also whil pulling with the manual.
With our diesels it's kind of a double edged sword. The 6 spd in my dad's truck is great with the exhaust brake and no worries about burning up OD with a stick. The downside is it seems the manual is slower to accelerate than the auto. This is due to the turbo lag mostly, but initial take off is also slower due to having to let out on a clutch and sometimes take out in granny when very heavy.
I can run in OD with my 47RE auto in my Ram Cummins but I now have a perfromance converter, valve body, and internals. I wouldn't tow much in OD with a stock auto with much weight. My auto is nice if I have to tow a lot in town. I also find my auto to be somewhat better in the mountains pulling our sled trailer, I don't have to constantly shift.
I don't even think you can get anything but a 4L65E in an HD1500, GM pretty much did away with a manual transmission in anything but a 3/4or 1 ton. The 4L65E will be just fine with a K5 on a trailer, and is probably your only option anyway with that model.