Which truck would be better for my TT

I estimate you are loaded for a long weekend with the family at 8500 pounds and 1100 pounds of TW. Besides tow ratings, you will probably want at least 1800 pounds of payload available with a family inside and a bed full of camping gear. The Tundra would work if you as a driver weigh less than 100 pounds and you keep the rest of the cab and bed empty. The F-150 as listed is borderline. If you can find/order a max paylaod F-150, you'll gain another 400-500 pounds of payload would I can then recommend. They are needle in the haystacks on dealer lots. Meanwhile, every 3/4 ton gas and most 3/4 ton diesels have 2000+ pounds of payload. You gain a lot in suspension and drivetrain (not so much power with the 3/4 ton gas) that makes the towing experience comfortable. They all also (3/4+ ton) come with LT tires, longer lasting brakes, and other heavier duty components that make total cost of ownership over 200k miles much more bearable. Fuel will be more.

We put 18-20k miles on our 3/4 ton Suburban which is our main family hauler, TV, and wife's daily driver in suburbia.