3/4 ton trucks have 6000-6500 RAWR which runs around 2800-3200 lb payload in the bed. These trucks are good for up to around 12k trailers. However much depends on dry weights and CCC numbers. Some trailers may have 3k-4k CCC numbers.
I pull a 11200 lb 5er with my '03 2500 Dodge/Cummins with no problems anywhere and the truck is well under all axle/tire weights.
Our one ton SRW trucks have 7000-7050 RAWR for around 3500-4000 lb payload in the bed. Same engine tranny so no issues pulling 15k 5th wheel trailers.
And of course the one ton DRW has those big 9350-9800 rawr for over 6k lb payloads in the bed. Some have over 30000 lb tow ratings.
The diesel will have no problems with any of the listed tow ratings. Many 6.4....6.0.....6.2 gas owners report no problems up to around 12k lbs.
Hard to say how much a certain 3/4 or one ton truck truck will handle. You will have to look at each trucks tow ratings...axle loads...gas or diesel engine/etc.
