IIRC, the HDs only got a bigger radiator on the gassers. the diesels are the same size, but IMHO cool slightly better, due to the lower part receiving more air than what the nostrils provide.
the HDs are rated for 15K GVWR. I will look up the GCWR for you if you would like, but it will be low. GM either used the 6.5L or the transmissions as the limiting factor. IMHO, the HD chassis is good for quite a bit more with the 4 wheel discs and the big frame.
what transmission do you have? both might require better cooling for long distance tows. they make some cool PTO finned covers for the 5 speed.
what trailer will you pull? gonna put a bed on, or just flaps, lights, and quarter fenders? is that the 159.5 inch wheelbase that takes the 11 foot bed?
one thing to watch out for is that rear end. in the owners manual, it will tell you that severe use (towing, running over 45 mph, running near max GVWR, etc) to change the conventional gear oil ever 3K miles. synthetic oil? every 30K miles. The reason is due to some desgn flaw in the axle that puts alot of stress on the ring gear carrier bearings or something like that. I would say some amsoil from a vendor and a mag-hytec diff cover would go a long ways towards sucess.
If I interpret the law correctly, it isnt what you weigh, but what you could weigh that matters to the DOT, so if I was you, I would find a trailer with dual 5200 lbs axles (or if you are friendly with a trailer mfg, get them to stamp it for 5200 axles, and run 7K axles for bigger bearings) I did spec out but never ordered a Kaufman 25 foot bumper pull with 5200lb axles, and it was pretty affordable. otherwise, any bigger than 5200lb, you are over 26K GCWR.
otherwise, do as the others suggested, if it isnt spin on, upgrade it, make sure the rad is clean and fan engages, etc.
good luck!