This is all going to depend on specific brand and year but....
Most 3/4 or 1 ton trucks will have a much heavier frame than a half ton equivalent. This will add rigidity and torsional strength for pulling loads.
Most will have larger axles and better gearing. This will help by having more gear fluid to better dissipate heat generated by towing and upgraded axles that are better able to handle loads.
Most will have much larger brakes which will help to stop the load.
Most will have much beefier and higher rate suspensions which will help support and control the loads better while towing.
All of these upgrades will result in a higher vehicle weight which will help control stopping heavier loads by countering "load push"
Duallies tow better because they have more surface area in contact with the road.
Your truck will not compare to a similar year F250 with a 5.4 when towing any moderately heavy load.
This.
My experience is with 2500 suburbans from 1993 - 2001, and my 2500 avalanche.
These are the differences I note in the 2500.
4L80/ 4L85 transmission over the 4L60, auxiliary trans cooler in addition to the one in the radiator.
Bigger frames, brakes, heavier springs, stiffer shocks
Axles and u joints are bigger and hold more oil. Bigger bearings in the axles that last longer under load.
Some 1500s and 2500s share the same motor, but the big differences come with the larger engines.
6.0/454/8.1L. Not only offer increase hp & tq, but offer better compression braking as well. The big block engines also hold more oil and water.
2500s also have bigger radiators that help keep the engines cooler when pulling long grades in hot weather.
Different fans, and different fan clutches that lock up sooner.
In addition to bigger brakes at the wheels, most 2500s have larger ps pumps with coolers and have hydroboost master cylinders.
These get the brake pressure above what is capable with manual, or vacuum assisted brakes.
On our 01 suburban, tow/haul mode does nothing, and never has made a noticeable difference.
On my 04 avalanche, it is a night and day difference, giving higher rpm shift points, with mph minimums for each gear, and much firmer and faster shifts. It will also hold out of overdrive until over 65 mph.
Don't know if the tow haul mode on 1/2 tons does the same or not. Definitely reduces the time hunting for a gear on the long grades at hwy speeds.
Huge difference going from Load range C tires to 8/10 ply load range d/e tires.
I have never seen a 2500 get better fuel mileage than the 1500 comparable truck.
Unloaded, the smaller motors get better fuel mileage, and the opposite is true towing.
Ex:
01 2500 6.0, 265 tires, 3.73 ratio gets 13-15 mpg empty hwy, 6-9 mpg towing on flat ground, and 3-5 mpg in the hills. Gets 11-13 towing 3k lbs.
97 2500 7.4L, 285 tires, 4.10 ratio gets 13-15 empty hwy, 7-10 mpg towing on flat ground, and 5-9 in the hills. Gets 11-13 towing 3k lbs
04 2500 8.1L, 285 tires, 4.10 ratio, 14 hwy empty, 9mpg city empty, 8-10 towing on flat, and 6-9 mpg towing in the hills. Get the same as empty, towing 3k lbs.
Those figures are hand calculated with towing 7-9k lbs.
'12 1500 5.3, 3.42 gears gets 19-20 mpg on the highway empty, but dropped to 12-15 towing 3000lbs on the highway.