If you're going to be hauling a gooseneck stock trailer over long distances, a diesel is a better choice. Diesel motors will produce more torque for towing and will use less fuel when carrying heavy loads. Gas motors may be lower in initial cost but they use more fuel and will last less long under heavy loads.
Duramax is tough and smooth but can possibly cost more to repair. Cummins is durable and simple but the truck it's in can suffer from issues. Powerstroke is high-towing power and there are many different types of trucks to choose from.
2 wheel drive is lighter and cheaper. 4 wheel drive is more traction in the mountains, snow, or mud but heavier and cheaper. Since you will be towing in the Rockies, 4 wheel drive will pay dividends for you.
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Ford with a Powerstroke would be an excellent choice for your needs.