Never say never, BUT.... I would NEVER get a 3/4 ton. They ALL have a 10,000 GVWR. Now-a-days, they can all pull over 16,000lbs! ...and have great GCWR up to 22,000lbs and OVER! Crazy and very, very capable, but if you look at the yellow door sticker on any of those trucks with any kind of cab and bed and you're gunna see 1700lbs, 1900lbs MAX payload. Now you put yourself, your cat and all your tools and hitch and gear... AND you won't have 1000lbs for the pin weight. You're 100% on when you say get the 4.10 gears in the Chevy and Ram, get the 4.30 in the Ford (for the gas version.) ...but again, sorry the Chevy is the DOG in this class with the WORST max carry of only 14,000ish lbs EVEN in a 1 ton! (again we're talking gasser's here.)
Ford 6.2L with 4.30 rear, OR Ram 6.4L with 4.10 whatever cab or package you like. I'm a SuperCab Long Bed man myself. Both will have 3500 - 4000lbs payloads, 14,000 trailer/15,500 5th wheel and 23,000 GCWR. Put some bags on it and DRIVE IT LIKE YOU STOLE IT!!
Just my VERY NARROW 2 cents worth.... Do what YOU like and Happy Hunting.