The heavy duty F-150 with tow package, 3.5L Ecoboost, and other high GVWR packages, Ford rates them to carry almost 3,000 pounds. The F-250 has about the same capacity, even with it's much higher GVWR, the truck base weight is much higher.
In 2015, the F-150 will have a all aluminum body, and you might want to wait until August to get one of those. The body can not rust through, and will be about 200 - 300 pounds lighter than the 2014.
As for mounting the hitch, that should be able to happen with either truck.
What will be the dry hitch weight?
How much do you plan on putting in the truck while camping?
Those two answers will be part of if the F-150 will be acceptable. If you have a heavy family, and want to carry a lot in the truck, then the F-350's 4,000 pound cargo rating will get the job done. With the F-150 or F-250, you would need a calculator to figure out if you will be fine or not.
By heavy family, I am stating that you might have 2 adults at 200 or so pounds each, and three kids around 120 - 150 pounds each. It all adds up to something around 700 - 800 pounds. That can take away a lot of the F-150's cargo rating, while it will hardly effect the F-350 cargo rating.
Best thing to do is read the towing guide, and understand what can be put into the trucks. You might also need to go to another local Ford dealer, they might be ordering more of the 3.5L F-150 with heavy duty towing package.
Once the new aluminum body comes out, then the Ford dealers will have a more difficult time pushing the older steel body trucks, you might get a better deal on one.
Fred.
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