If I was moving up right now, it would be a Ram. The 6.4 is the better motor because it takes 87 Octane (recommended), gets decent mileage non towing with cylinder deactivation, and has more power (410 HP). The 5.7 will probably be similar in feel to the Tundra with 383 HP. It has similar power, just make sure you buy one with an appropriate rear axle ratio for towing. You can probably find more 5.7s than 6.4s right now, especially if you look used. The "downfalls" are similar power with a heavier chassis and I believe the 5.7 is recommended with 89 Octane gas.
Either engine would be fine. With a gas engine you will also get substantially more payload than a diesel. Properly configured you can get a 3/4 ton with roughly the same payload as some 1 tons, somewhere in the neighborhood of 3000 lbs, which will roughly DOUBLE your payload from a Tundra.
The Ford 6.2 is a proven engine and makes decent power. I like the current model SuperDuty trucks too. Good power (385 HP I think) and acceptable fuel economy in the heavier truck. Can't go wrong there.
I do not like GM and avoid them as much as I can, but the 6.0 gas engine is decent enough. Less horsepower and torque than your Tundra though, so it won't feel as powerful... but honestly 360 hp is still a lot of power. My father in law has a 6.0 and tows about the same weight as you do.
Take your pick, you won't go wrong.